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Berapa hasil dari
200
⋅
201
⋅
202
⋅
203
)
+
1
{\displaystyle {\sqrt {200\cdot 201\cdot 202\cdot 203)+1}}}
Jawaban
200
⋅
201
⋅
202
⋅
203
)
+
1
=
200
(
200
+
1
)
(
200
+
2
)
(
200
+
3
)
+
1
misalkan 200=x
=
x
(
x
+
1
)
(
x
+
2
)
(
x
+
3
)
+
1
=
x
(
x
+
3
)
(
x
+
1
)
(
x
+
2
)
+
1
=
(
x
2
+
3
x
)
(
x
2
+
3
x
+
2
)
+
1
misalkan
x
2
+
3
x
=
n
=
n
(
n
+
2
)
+
1
=
n
2
+
2
n
+
1
=
(
n
+
1
)
2
=
n
+
1
=
x
2
+
3
x
+
1
=
200
2
+
3
(
200
)
+
1
=
40.000
+
600
+
1
=
40.601
{\displaystyle {\begin{aligned}{\sqrt {200\cdot 201\cdot 202\cdot 203)+1}}&={\sqrt {200(200+1)(200+2)(200+3)+1}}\\{\text{misalkan 200=x }}\\&={\sqrt {x(x+1)(x+2)(x+3)+1}}\\&={\sqrt {x(x+3)(x+1)(x+2)+1}}\\&={\sqrt {(x^{2}+3x)(x^{2}+3x+2)+1}}\\{\text{misalkan }}x^{2}+3x=n\\&={\sqrt {n(n+2)+1}}\\&={\sqrt {n^{2}+2n+1}}\\&={\sqrt {(n+1)^{2}}}\\&=n+1\\&=x^{2}+3x+1\\&=200^{2}+3(200)+1\\&=40.000+600+1\\&=40.601\\\end{aligned}}}
Berapa hasil dari
1
1
×
2
+
1
2
×
3
+
1
3
×
4
+
⋯
+
1
2023
×
2024
{\displaystyle {\frac {1}{1\times 2}}+{\frac {1}{2\times 3}}+{\frac {1}{3\times 4}}+\dots +{\frac {1}{2023\times 2024}}}
Jawaban
Cara 1
Perhatian
1
n
×
(
n
+
1
)
=
1
n
−
1
n
+
1
1
1
×
2
+
1
2
×
3
+
1
3
×
4
+
⋯
+
1
2023
×
2024
=
(
1
1
−
1
2
)
+
(
1
2
−
1
3
)
+
(
1
3
−
1
4
)
+
⋯
+
(
1
2023
−
1
2024
)
=
1
−
1
2024
=
2024
2024
−
1
2024
=
2024
−
1
2024
=
2023
2024
Cara 2
1
1
×
2
+
1
2
×
3
+
1
3
×
4
+
⋯
+
1
n
×
(
n
+
1
)
=
n
n
+
1
1
1
×
2
+
1
2
×
3
+
1
3
×
4
+
⋯
+
1
2023
×
2024
=
2023
2024
{\displaystyle {\begin{aligned}{\text{Cara 1 }}\\{\text{Perhatian }}{\frac {1}{n\times (n+1)}}&={\frac {1}{n}}-{\frac {1}{n+1}}\\{\frac {1}{1\times 2}}+{\frac {1}{2\times 3}}+{\frac {1}{3\times 4}}+\dots +{\frac {1}{2023\times 2024}}&=({\frac {1}{1}}-{\frac {1}{2}})+({\frac {1}{2}}-{\frac {1}{3}})+({\frac {1}{3}}-{\frac {1}{4}})+\dots +({\frac {1}{2023}}-{\frac {1}{2024}})\\&=1-{\frac {1}{2024}}\\&={\frac {2024}{2024}}-{\frac {1}{2024}}\\&={\frac {2024-1}{2024}}\\&={\frac {2023}{2024}}\\{\text{Cara 2 }}\\{\frac {1}{1\times 2}}+{\frac {1}{2\times 3}}+{\frac {1}{3\times 4}}+\dots +{\frac {1}{n\times (n+1)}}&={\frac {n}{n+1}}\\{\frac {1}{1\times 2}}+{\frac {1}{2\times 3}}+{\frac {1}{3\times 4}}+\dots +{\frac {1}{2023\times 2024}}&={\frac {2023}{2024}}\\\end{aligned}}}
Berapa hasil dari
6
+
6
+
6
+
…
{\displaystyle {\sqrt {6+{\sqrt {6+{\sqrt {6+\dots }}}}}}}
Jawaban
6
+
6
+
6
+
…
=
x
(
6
+
6
+
6
+
…
)
2
=
x
2
6
+
(
6
+
6
+
…
)
=
x
2
6
+
x
=
x
2
x
2
−
x
−
6
=
0
(
x
−
3
)
(
x
−
2
)
=
0
x
=
3
atau
x
=
−
2
jadi x adalah
3
{\displaystyle {\begin{aligned}{\sqrt {6+{\sqrt {6+{\sqrt {6+\dots }}}}}}&=x\\({\sqrt {6+{\sqrt {6+{\sqrt {6+\dots }}}}}})^{2}&=x^{2}\\6+({\sqrt {6+{\sqrt {6+\dots }}}})&=x^{2}\\6+x&=x^{2}\\x^{2}-x-6&=0\\(x-3)(x-2)&=0\\x=3&{\text{ atau }}x=-2\\{\text{ jadi x adalah }}3\\\end{aligned}}}
Berapa hasil dari
20
−
20
−
20
−
…
{\displaystyle {\sqrt {20-{\sqrt {20-{\sqrt {20-\dots }}}}}}}
Jawaban
20
−
20
+
20
−
…
=
x
(
20
−
20
−
20
−
…
)
2
=
x
2
20
−
(
20
−
20
−
…
)
=
x
2
20
−
x
=
x
2
x
2
+
x
−
20
=
0
(
x
−
4
)
(
x
+
5
)
=
0
x
=
4
atau
x
=
−
5
jadi x adalah
4
{\displaystyle {\begin{aligned}{\sqrt {20-{\sqrt {20+{\sqrt {20-\dots }}}}}}&=x\\({\sqrt {20-{\sqrt {20-{\sqrt {20-\dots }}}}}})^{2}&=x^{2}\\20-({\sqrt {20-{\sqrt {20-\dots }}}})&=x^{2}\\20-x&=x^{2}\\x^{2}+x-20&=0\\(x-4)(x+5)&=0\\x=4&{\text{ atau }}x=-5\\{\text{ jadi x adalah }}4\\\end{aligned}}}
Berapa hasil dari
2
2
2
…
{\displaystyle {\sqrt {2{\sqrt {2{\sqrt {2\dots }}}}}}}
Jawaban
2
2
2
…
=
x
2
2
2
…
=
x
2
maka menjadi
x
2
x
=
2
2
2
…
2
2
2
…
x
=
2
{\displaystyle {\begin{aligned}{\sqrt {2{\sqrt {2{\sqrt {2\dots }}}}}}&=x\\2{\sqrt {2{\sqrt {2\dots }}}}&=x^{2}\\{\text{maka menjadi }}{\frac {x^{2}}{x}}&={\frac {2{\sqrt {2{\sqrt {2\dots }}}}}{\sqrt {2{\sqrt {2{\sqrt {2\dots }}}}}}}\\x&=2\\\end{aligned}}}
Berapa hasil dari
8
8
8
…
{\displaystyle {\sqrt {\frac {8}{\sqrt {\frac {8}{\sqrt {\frac {8}{\dots }}}}}}}}
Jawaban
8
8
8
…
=
x
8
8
8
…
=
x
2
8
x
=
x
2
x
3
=
8
x
=
8
3
x
=
2
{\displaystyle {\begin{aligned}{\sqrt {\frac {8}{\sqrt {\frac {8}{\sqrt {\frac {8}{\dots }}}}}}}&=x\\{\frac {8}{\sqrt {\frac {8}{\sqrt {\frac {8}{\dots }}}}}}&=x^{2}\\{\frac {8}{x}}&=x^{2}\\x^{3}&=8\\x&={\sqrt[{3}]{8}}\\x&=2\\\end{aligned}}}
Berapa hasil dari
3
3
3
3
{\displaystyle {\sqrt {3{\sqrt {3{\sqrt {3{\sqrt {3}}}}}}}}}
Jawaban
Cara 1
3
3
3
3
=
3
3
3
×
3
1
2
=
3
3
3
3
2
=
3
3
×
3
3
4
=
3
3
7
4
=
3
×
3
7
8
=
3
15
8
=
3
15
16
=
3
15
16
Cara 2
Gunakan rumus
a
2
n
−
1
2
n
n adalah banyaknya akar
3
3
3
3
=
3
2
4
−
1
2
4
=
3
16
−
1
16
=
3
15
16
=
3
15
16
{\displaystyle {\begin{aligned}{\text{Cara 1}}\\{\sqrt {3{\sqrt {3{\sqrt {3{\sqrt {3}}}}}}}}&={\sqrt {3{\sqrt {3{\sqrt {3\times 3^{\frac {1}{2}}}}}}}}\\&={\sqrt {3{\sqrt {3{\sqrt {3^{\frac {3}{2}}}}}}}}\\&={\sqrt {3{\sqrt {3\times 3^{\frac {3}{4}}}}}}\\&={\sqrt {3{\sqrt {3^{\frac {7}{4}}}}}}\\&={\sqrt {3\times 3^{\frac {7}{8}}}}\\&={\sqrt {3^{\frac {15}{8}}}}\\&=3^{\frac {15}{16}}\\&={\sqrt[{16}]{3^{15}}}\\{\text{Cara 2}}\\{\text{Gunakan rumus }}a^{\frac {2^{n}-1}{2^{n}}}{\text{ n adalah banyaknya akar }}{\sqrt {3{\sqrt {3{\sqrt {3{\sqrt {3}}}}}}}}&=3^{\frac {2^{4}-1}{2^{4}}}\\&=3^{\frac {16-1}{16}}\\&=3^{\frac {15}{16}}\\&={\sqrt[{16}]{3^{15}}}\\\end{aligned}}}
Berapa nilai x dari
4
x
+
4
x
+
4
x
+
…
=
9
{\displaystyle {\sqrt {4x+{\sqrt {4x+{\sqrt {4x+\dots }}}}}}=9}
Jawaban
4
x
+
4
x
+
4
x
+
…
=
9
(
4
x
+
4
x
+
4
x
+
…
)
2
=
(
9
)
2
4
x
+
(
4
x
+
4
x
+
…
)
=
81
4
x
+
9
=
81
4
x
=
72
x
=
13
{\displaystyle {\begin{aligned}{\sqrt {4x+{\sqrt {4x+{\sqrt {4x+\dots }}}}}}&=9\\({\sqrt {4x+{\sqrt {4x+{\sqrt {4x+\dots }}}}}})^{2}&=(9)^{2}\\4x+({\sqrt {4x+{\sqrt {4x+\dots }}}})&=81\\4x+9&=81\\4x&=72\\x&=13\\\end{aligned}}}
Berapa nilai x dari
7
x
+
2
−
7
x
+
2
−
7
x
+
2
−
…
=
12
{\displaystyle {\sqrt {7x+2-{\sqrt {7x+2-{\sqrt {7x+2-\dots }}}}}}=12}
Jawaban
7
x
+
2
−
7
x
+
2
−
7
x
+
2
−
…
=
12
(
7
x
+
2
−
7
x
+
2
−
7
x
+
2
−
…
)
2
=
(
12
)
2
7
x
+
2
−
(
7
x
+
2
−
7
x
+
2
−
…
)
=
144
7
x
+
2
−
12
=
144
7
x
=
154
x
=
22
{\displaystyle {\begin{aligned}{\sqrt {7x+2-{\sqrt {7x+2-{\sqrt {7x+2-\dots }}}}}}&=12\\({\sqrt {7x+2-{\sqrt {7x+2-{\sqrt {7x+2-\dots }}}}}})^{2}&=(12)^{2}\\7x+2-({\sqrt {7x+2-{\sqrt {7x+2-\dots }}}})&=144\\7x+2-12&=144\\7x&=154\\x&=22\\\end{aligned}}}
Berapa hasil dari
1
2
+
3
1
2
+
3
1
2
+
3
…
{\displaystyle {\frac {1}{2+3{\frac {1}{2+3{\frac {1}{2+3\dots }}}}}}}
Jawaban
1
2
+
3
1
2
+
3
1
2
+
3
…
=
Misalkan
1
2
+
3
1
2
+
3
…
=
x
1
2
+
3
x
=
x
1
=
x
(
2
+
3
x
)
1
=
2
x
+
3
x
2
3
x
2
+
2
x
−
1
=
0
(
3
x
−
1
)
(
x
+
1
)
=
0
x
=
1
3
atau
x
=
−
1
{\displaystyle {\begin{aligned}{\frac {1}{2+3{\frac {1}{2+3{\frac {1}{2+3\dots }}}}}}=\\{\text{Misalkan }}{\frac {1}{2+3{\frac {1}{2+3\dots }}}}&=x\\{\frac {1}{2+3x}}&=x\\1&=x(2+3x)\\1&=2x+3x^{2}\\3x^{2}+2x-1&=0\\(3x-1)(x+1)&=0\\x={\frac {1}{3}}&{\text{ atau }}x=-1\\\end{aligned}}}
Berapa hasil dari
7
+
16
1
+
56
1
+
56
1
+
56
1
+
…
{\displaystyle 7+{\frac {16}{1+{\frac {56}{1+{\frac {56}{1+{\frac {56}{1+\dots }}}}}}}}}
Jawaban
7
+
16
1
+
56
1
+
56
1
+
56
1
+
…
=
Misalkan
1
+
56
1
+
…
=
x
1
+
56
x
=
x
x
+
56
=
x
2
x
2
−
x
−
56
=
0
(
x
−
8
)
(
x
+
7
)
=
0
x
=
8
atau
x
=
−
7
Karena hasilnya selalu bilangan positif jadi
x
=
8
7
+
16
8
=
7
+
2
=
9
{\displaystyle {\begin{aligned}7+{\frac {16}{1+{\frac {56}{1+{\frac {56}{1+{\frac {56}{1+\dots }}}}}}}}=\\{\text{Misalkan }}1+{\frac {56}{1+\dots }}&=x\\1+{\frac {56}{x}}&=x\\x+56&=x^{2}\\x^{2}-x-56&=0\\(x-8)(x+7)&=0\\x=8&{\text{ atau }}x=-7\\{\text{Karena hasilnya selalu bilangan positif jadi }}x=8\\7+{\frac {16}{8}}&=7+2=9\\\end{aligned}}}
Berapa hasil dari
x
2
−
3
x
y
+
y
2
{\displaystyle x^{2}-3xy+y^{2}}
Jawaban
x
2
−
3
x
y
+
y
2
=
x
2
+
2
x
y
+
y
2
−
5
x
y
=
(
x
+
y
)
2
−
5
x
y
=
7
2
−
5
(
−
4
)
=
49
+
20
=
69
{\displaystyle {\begin{aligned}x^{2}-3xy+y^{2}&=x^{2}+2xy+y^{2}-5xy\\&=(x+y)^{2}-5xy\\&=7^{2}-5(-4)\\&=49+20\\&=69\\\end{aligned}}}
Berapa hasil dari
2027
×
(
2025
2
−
9
)
×
2023
2028
×
(
2025
2
−
4
)
{\displaystyle {\frac {2027\times (2025^{2}-9)\times 2023}{2028\times (2025^{2}-4)}}}
Jawaban
2027
×
(
2025
2
−
9
)
×
2023
2028
×
(
2025
2
−
4
)
misalkan x=2025
(
x
+
2
)
×
(
x
2
−
9
)
×
(
x
−
2
)
(
x
+
3
)
×
(
x
2
−
4
)
(
x
−
3
)
×
(
x
+
3
)
×
(
x
2
−
4
)
(
x
+
3
)
×
(
x
2
−
4
)
x
−
3
2025
−
3
2022
{\displaystyle {\begin{aligned}{\frac {2027\times (2025^{2}-9)\times 2023}{2028\times (2025^{2}-4)}}\\{\text{misalkan x=2025 }}\\{\frac {(x+2)\times (x^{2}-9)\times (x-2)}{(x+3)\times (x^{2}-4)}}\\{\frac {(x-3)\times (x+3)\times (x^{2}-4)}{(x+3)\times (x^{2}-4)}}\\x-3\\2025-3\\2022\\\end{aligned}}}
Berapa hasil x dari
x
−
10
2023
+
x
−
9
2024
+
x
−
8
2025
=
3
{\displaystyle {\frac {x-10}{2023}}+{\frac {x-9}{2024}}+{\frac {x-8}{2025}}=3}
Jawaban
x
−
10
2023
+
x
−
9
2024
+
x
−
8
2025
=
3
x
−
10
2023
+
x
−
9
2024
+
x
−
8
2025
=
1
+
1
+
1
x
−
10
2023
−
1
+
x
−
9
2024
−
1
+
x
−
8
2025
−
1
=
0
x
−
10
−
2023
2023
+
x
−
9
−
2024
2024
+
x
−
8
−
2025
2025
=
0
x
−
2033
2023
+
x
−
2033
2024
+
x
−
2033
2025
=
0
(
x
−
2033
)
(
1
2023
+
1
2024
+
1
2025
)
=
0
x
−
2033
=
0
x
=
2033
{\displaystyle {\begin{aligned}{\frac {x-10}{2023}}+{\frac {x-9}{2024}}+{\frac {x-8}{2025}}&=3\\{\frac {x-10}{2023}}+{\frac {x-9}{2024}}+{\frac {x-8}{2025}}&=1+1+1\\{\frac {x-10}{2023}}-1+{\frac {x-9}{2024}}-1+{\frac {x-8}{2025}}-1&=0\\{\frac {x-10-2023}{2023}}+{\frac {x-9-2024}{2024}}+{\frac {x-8-2025}{2025}}&=0\\{\frac {x-2033}{2023}}+{\frac {x-2033}{2024}}+{\frac {x-2033}{2025}}&=0\\(x-2033)({\frac {1}{2023}}+{\frac {1}{2024}}+{\frac {1}{2025}})&=0\\x-2033&=0\\x&=2033\\\end{aligned}}}
Berapa hasil x dari
x
−
17
2026
+
x
−
19
2024
+
x
−
21
2022
=
3
{\displaystyle {\frac {x-17}{2026}}+{\frac {x-19}{2024}}+{\frac {x-21}{2022}}=3}
Jawaban
x
−
17
2026
+
x
−
19
2024
+
x
−
21
2022
=
3
x
−
17
2026
+
x
−
19
2024
+
x
−
21
2022
=
1
+
1
+
1
x
−
17
2026
−
1
+
x
−
19
2024
−
1
+
x
−
21
2022
−
1
=
0
x
−
17
−
2026
2026
+
x
−
19
−
2024
2024
+
x
−
21
−
2022
2022
=
0
x
−
2043
2026
+
x
−
2043
2024
+
x
−
2043
2022
=
0
(
x
−
2043
)
(
1
2026
+
1
2024
+
1
2022
)
=
0
x
−
2043
=
0
x
=
2043
{\displaystyle {\begin{aligned}{\frac {x-17}{2026}}+{\frac {x-19}{2024}}+{\frac {x-21}{2022}}&=3\\{\frac {x-17}{2026}}+{\frac {x-19}{2024}}+{\frac {x-21}{2022}}&=1+1+1\\{\frac {x-17}{2026}}-1+{\frac {x-19}{2024}}-1+{\frac {x-21}{2022}}-1&=0\\{\frac {x-17-2026}{2026}}+{\frac {x-19-2024}{2024}}+{\frac {x-21-2022}{2022}}&=0\\{\frac {x-2043}{2026}}+{\frac {x-2043}{2024}}+{\frac {x-2043}{2022}}&=0\\(x-2043)({\frac {1}{2026}}+{\frac {1}{2024}}+{\frac {1}{2022}})&=0\\x-2043&=0\\x&=2043\\\end{aligned}}}
Berapa banyaknya bilangan kurang dari atau sama dengan 50 yang memiliki 6 faktor? menggunakan pola bilangan prima seperti mencari kpk dan fpb.
kemungkinan pertama: p5 maka hanya 25 = 32 saja
kemungkinan kedua: p2 q maka beberapa kemungkinan sebagai berikut:
22 3 = 12, 22 5 = 20, 22 7 = 28, 22 11 = 44
32 2 = 18, 32 5 = 45
52 2 = 50 jadi banyaknya adalah 8. Dua dadu dilempar bersama-sama satu kali. Berapa peluang bahwa dua dadu yang muncul berangka sama? jumlah seluruh dadu (s) yaitu 6x6 = 36
dua dadu yang sama angkanya (a) yakni {(1,1), (2,2), (3,3), (4,4), (5,5), (6,6)} jadi ada 6
maka peluangnya adalah
P
(
a
)
=
6
36
=
1
6
{\displaystyle P(a)={\frac {6}{36}}={\frac {1}{6}}}
Jumlah kedua bilangan adalah 30 maka berapa nilai maksimum dari hasil kali kedua bilangan? Jumlah kedua bilangan yang menghasilkan 30 yang mungkin adalah (0,30), (1,29), (2,28), (3,27), …., (15,15)
Hasil kali kedua bilangan masing-masing yakni 0, 29, 56, 81, 104, 125, …., 225
Jadi hasil kali yang paling maksimum adalah 225 Berapa angka desimal ke 2024 jika hasil dari 1/7? Hasil dari 1/7 adalah 0,142857142857…
Karena berulang-ulang keenam angka yang sama maka sisa dari 2024 dibagi 6 yaitu 0. angka 0 berarti 7. Berapa angka desimal ke 2024 jika hasil dari 1/13? Hasil dari 1/13 adalah 0,076923076923…
Karena berulang-ulang keenam angka yang sama maka sisa dari 2024 dibagi 6 yaitu 0. angka 0 berarti 3. Dua persamaan yaitu 43a+20b-10c=36 dan 2a-2b+19c=-9 maka berapa hasil dari 5a+2b+c? Jawaban
43
a
+
20
b
−
10
c
=
36
2
a
−
2
b
+
19
c
=
−
9
45
a
+
18
b
+
9
c
=
27
(persamaan (1) ditambahkan (2))
5
a
+
2
b
+
c
=
3
{\displaystyle {\begin{aligned}43a+20b-10c&=36\\2a-2b+19c&=-9\\45a+18b+9c&=27{\text{ (persamaan (1) ditambahkan (2))}}\\5a+2b+c&=3\\\end{aligned}}}
Berapa hasil f(16)-f(7) dari f(3x-2)=4x-7? Jawaban
f
(
16
)
=
f
(
3
x
−
2
)
16
=
3
x
−
2
3
x
=
18
x
=
6
f
(
16
)
=
4
(
6
)
−
7
=
17
f
(
7
)
=
f
(
3
x
−
2
)
7
=
3
x
−
2
3
x
=
9
x
=
3
f
(
7
)
=
4
(
3
)
−
7
=
5
f
(
16
)
−
f
(
7
)
=
17
−
5
=
12
{\displaystyle {\begin{aligned}f(16)&=f(3x-2)\\16&=3x-2\\3x&=18\\x&=6\\f(16)&=4(6)-7\\&=17\\f(7)&=f(3x-2)\\7&=3x-2\\3x&=9\\x&=3\\f(7)&=4(3)-7\\&=5\\f(16)-f(7)&=17-5\\&=12\\\end{aligned}}}
Sebuah persegi memiliki dua persegi panjang secara sembarangan baik vertikal atau horisontal. jika keliling kedua persegi panjang adalah 102 meter maka berapa luas persegi? Jawaban
b
=
a
+
c
k
=
2
(
a
+
b
)
+
2
(
b
+
c
)
102
=
2
a
+
4
b
+
2
c
51
=
a
+
2
b
+
c
51
=
b
+
2
b
51
=
3
b
b
=
17
l
=
b
2
=
17
2
=
289
m
2
{\displaystyle {\begin{aligned}b&=a+c\\k&=2(a+b)+2(b+c)\\102&=2a+4b+2c\\51&=a+2b+c\\51&=b+2b\\51&=3b\\b&=17\\l&=b^{2}\\&={17}^{2}\\&=289m^{2}\\\end{aligned}}}
![{\displaystyle {\begin{aligned}{\sqrt {\frac {8}{\sqrt {\frac {8}{\sqrt {\frac {8}{\dots }}}}}}}&=x\\{\frac {8}{\sqrt {\frac {8}{\sqrt {\frac {8}{\dots }}}}}}&=x^{2}\\{\frac {8}{x}}&=x^{2}\\x^{3}&=8\\x&={\sqrt[{3}]{8}}\\x&=2\\\end{aligned}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/cc7b5bfd2cd24a9478e1ae4884edbeea157023a2)
![{\displaystyle {\begin{aligned}{\text{Cara 1}}\\{\sqrt {3{\sqrt {3{\sqrt {3{\sqrt {3}}}}}}}}&={\sqrt {3{\sqrt {3{\sqrt {3\times 3^{\frac {1}{2}}}}}}}}\\&={\sqrt {3{\sqrt {3{\sqrt {3^{\frac {3}{2}}}}}}}}\\&={\sqrt {3{\sqrt {3\times 3^{\frac {3}{4}}}}}}\\&={\sqrt {3{\sqrt {3^{\frac {7}{4}}}}}}\\&={\sqrt {3\times 3^{\frac {7}{8}}}}\\&={\sqrt {3^{\frac {15}{8}}}}\\&=3^{\frac {15}{16}}\\&={\sqrt[{16}]{3^{15}}}\\{\text{Cara 2}}\\{\text{Gunakan rumus }}a^{\frac {2^{n}-1}{2^{n}}}{\text{ n adalah banyaknya akar }}{\sqrt {3{\sqrt {3{\sqrt {3{\sqrt {3}}}}}}}}&=3^{\frac {2^{4}-1}{2^{4}}}\\&=3^{\frac {16-1}{16}}\\&=3^{\frac {15}{16}}\\&={\sqrt[{16}]{3^{15}}}\\\end{aligned}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/60f61f8bc80113e19dd6d2a148b6305fb80df226)
