What is expand (sqrt(2)+sqrt(3))^5 ?

The solution to expand (sqrt(2)+sqrt(3))^5 is 109sqrt(2)+89sqrt(3)

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expand (sqrt(2)+sqrt(3))^5

expand

(2 + 3)^{5}

1092 + 893

Decimal Notation

308.30180 \dots

Solution steps

(2 + 3)^{5}

Apply binomial theorem:

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

a = 2, b = 3

= i = 0 \sum 5 (i 5) (2)^{(5 - i)} (3)^{i}

Expand summation

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

Simplify

\frac{5 !}{0 ! ( 5 - 0 ) !} (2)^{5} (3)^{0} : 42

Simplify

\frac{5 !}{1 ! ( 5 - 1 ) !} (2)^{4} (3)^{1} : 203

Simplify

\frac{5 !}{2 ! ( 5 - 2 ) !} (2)^{3} (3)^{2} : 602

Simplify

\frac{5 !}{3 ! ( 5 - 3 ) !} (2)^{2} (3)^{3} : 603

Simplify

\frac{5 !}{4 ! ( 5 - 4 ) !} (2)^{1} (3)^{4} : 452

Simplify

\frac{5 !}{5 ! ( 5 - 5 ) !} (2)^{0} (3)^{5} : 93

= 42 + 203 + 602 + 603 + 452 + 93

42 + 203 + 602 + 603 + 452 + 93 = 1092 + 893

= 1092 + 893

- csc^{2} (x) cot (x) (csc^{2} (x) - cot (x))

18 π (1 + \frac{π}{4})

(x^{2} - \frac{3 y}{4} + \frac{9}{7}) (\frac{x}{2} + \frac{3 y}{5} - 2)

h (4 x + h + 4 x)

(1 + x - 5)^{2}

What is expand (sqrt(2)+sqrt(3))^5 ?
The solution to expand (sqrt(2)+sqrt(3))^5 is 109sqrt(2)+89sqrt(3)