What is expand (sqrt(5)+sqrt(7))^4 ?

The solution to expand (sqrt(5)+sqrt(7))^4 is 284+48sqrt(35)

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expand (sqrt(5)+sqrt(7))^4

expand

(5 + 7)^{4}

284 + 4835

Decimal Notation

567.97182 \dots

Solution steps

(5 + 7)^{4}

Apply binomial theorem:

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

a = 5, b = 7

= i = 0 \sum 4 (i 4) (5)^{(4 - i)} (7)^{i}

Expand summation

= \frac{4 !}{0 ! ( 4 - 0 ) !} (5)^{4} (7)^{0} + \frac{4 !}{1 ! ( 4 - 1 ) !} (5)^{3} (7)^{1} + \frac{4 !}{2 ! ( 4 - 2 ) !} (5)^{2} (7)^{2} + \frac{4 !}{3 ! ( 4 - 3 ) !} (5)^{1} (7)^{3} + \frac{4 !}{4 ! ( 4 - 4 ) !} (5)^{0} (7)^{4}

Simplify

\frac{4 !}{0 ! ( 4 - 0 ) !} (5)^{4} (7)^{0} : 25

Simplify

\frac{4 !}{1 ! ( 4 - 1 ) !} (5)^{3} (7)^{1} : 2035

Simplify

\frac{4 !}{2 ! ( 4 - 2 ) !} (5)^{2} (7)^{2} : 210

Simplify

\frac{4 !}{3 ! ( 4 - 3 ) !} (5)^{1} (7)^{3} : 2835

Simplify

\frac{4 !}{4 ! ( 4 - 4 ) !} (5)^{0} (7)^{4} : 49

= 25 + 2035 + 210 + 2835 + 49

25 + 2035 + 210 + 2835 + 49 = 284 + 4835

= 284 + 4835

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What is expand (sqrt(5)+sqrt(7))^4 ?
The solution to expand (sqrt(5)+sqrt(7))^4 is 284+48sqrt(35)