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

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

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

expand

(3 + 2)^{5}

893 + 1092

Decimal Notation

308.30180 \dots

Solution steps

(3 + 2)^{5}

Apply binomial theorem:

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

a = 3, b = 2

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

Expand summation

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

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

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

= 893 + 1092

122 (e^{(- 0.18 t)} - e^{(- t)})

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

(2 + e^{x})^{3}

8 x^{2} - (24 x + 9) ln (x)

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