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Popular >

expand (sqrt(2)+1)^6

Solution

expand

(2 + 1)^{6}

Solution

99 + 702

+1

Decimal Notation

197.99494 \dots

Solution steps

(2 + 1)^{6}

Apply binomial theorem:

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

a = 2, b = 1

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

Expand summation

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

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

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

= 99 + 702

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Frequently Asked Questions (FAQ)

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