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Popular >

expand (1+sqrt(2))^6

Solution

expand

(1 + 2)^{6}

Solution

99 + 702

+1

Decimal Notation

197.99494 \dots

Solution steps

(1 + 2)^{6}

Apply binomial theorem:

(a + b)^{n} = i = 0 \sum n (i n) a^{(n - i)} b^{i}

a = 1, b = 2

= i = 0 \sum 6 (i 6) \cdot 1^{(6 - i)} (2)^{i}

Expand summation

= \frac{6 !}{0 ! ( 6 - 0 ) !} \cdot 1^{6} (2)^{0} + \frac{6 !}{1 ! ( 6 - 1 ) !} \cdot 1^{5} (2)^{1} + \frac{6 !}{2 ! ( 6 - 2 ) !} \cdot 1^{4} (2)^{2} + \frac{6 !}{3 ! ( 6 - 3 ) !} \cdot 1^{3} (2)^{3} + \frac{6 !}{4 ! ( 6 - 4 ) !} \cdot 1^{2} (2)^{4} + \frac{6 !}{5 ! ( 6 - 5 ) !} \cdot 1^{1} (2)^{5} + \frac{6 !}{6 ! ( 6 - 6 ) !} \cdot 1^{0} (2)^{6}

Simplify

\frac{6 !}{0 ! ( 6 - 0 ) !} \cdot 1^{6} (2)^{0} : 1

Simplify

\frac{6 !}{1 ! ( 6 - 1 ) !} \cdot 1^{5} (2)^{1} : 62

Simplify

\frac{6 !}{2 ! ( 6 - 2 ) !} \cdot 1^{4} (2)^{2} : 30

Simplify

\frac{6 !}{3 ! ( 6 - 3 ) !} \cdot 1^{3} (2)^{3} : 402

Simplify

\frac{6 !}{4 ! ( 6 - 4 ) !} \cdot 1^{2} (2)^{4} : 60

Simplify

\frac{6 !}{5 ! ( 6 - 5 ) !} \cdot 1^{1} (2)^{5} : 242

Simplify

\frac{6 !}{6 ! ( 6 - 6 ) !} \cdot 1^{0} (2)^{6} : 8

= 1 + 62 + 30 + 402 + 60 + 242 + 8

1 + 62 + 30 + 402 + 60 + 242 + 8 = 99 + 702

= 99 + 702

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Frequently Asked Questions (FAQ)

What is expand (1+sqrt(2))^6 ?
The solution to expand (1+sqrt(2))^6 is 99+70sqrt(2)