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Popular >

expand (1+sqrt(3))^5

Solution

expand

(1 + 3)^{5}

Solution

76 + 443

+1

Decimal Notation

152.21023 \dots

Solution steps

(1 + 3)^{5}

Apply binomial theorem:

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

a = 1, b = 3

= i = 0 \sum 5 (i 5) \cdot 1^{(5 - i)} (3)^{i}

Expand summation

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

Simplify

\frac{5 !}{0 ! ( 5 - 0 ) !} \cdot 1^{5} (3)^{0} : 1

Simplify

\frac{5 !}{1 ! ( 5 - 1 ) !} \cdot 1^{4} (3)^{1} : 53

Simplify

\frac{5 !}{2 ! ( 5 - 2 ) !} \cdot 1^{3} (3)^{2} : 30

Simplify

\frac{5 !}{3 ! ( 5 - 3 ) !} \cdot 1^{2} (3)^{3} : 303

Simplify

\frac{5 !}{4 ! ( 5 - 4 ) !} \cdot 1^{1} (3)^{4} : 45

Simplify

\frac{5 !}{5 ! ( 5 - 5 ) !} \cdot 1^{0} (3)^{5} : 93

= 1 + 53 + 30 + 303 + 45 + 93

1 + 53 + 30 + 303 + 45 + 93 = 76 + 443

= 76 + 443

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Frequently Asked Questions (FAQ)

What is expand (1+sqrt(3))^5 ?
The solution to expand (1+sqrt(3))^5 is 76+44sqrt(3)