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

\frac{x - 4 \cdot x + 4}{( x - 2 ) ( x - 4 )}

\frac{6 x ^{2} + 7 x + 9}{3 x}

\frac{( a - x ) ^{4}}{4}

4 (3 cos (t) + 1) - (3 sin (t) + 3)^{2} sin (3 cos (t) + 1)

\frac{s ^{2} + 4 s + 2}{s ( s + 2 ) ( s + 4 )}

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