What is 2/((sqrt(3)+2)^2) ?

The solution to 2/((sqrt(3)+2)^2) is 14-8sqrt(3)

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simplify 2/((sqrt(3)+2)^2)

simplify

\frac{2}{( 3 + 2 ) ^{2}}

14 - 83

Solution steps

\frac{2}{( 3 + 2 ) ^{2}}

Expand

(3 + 2)^{2} : 7 + 43

= \frac{2}{7 + 4 3}

Multiply by the conjugate

\frac{7 - 4 3}{7 - 4 3}

= \frac{2 ( 7 - 4 3 )}{( 7 + 4 3 ) ( 7 - 4 3 )}

Expand

2 (7 - 43) : 14 - 83

Expand

(7 + 43) (7 - 43) : 1

= \frac{14 - 8 3}{1}

Apply the fraction rule:

\frac{a}{1} = a

= 14 - 83

2 (2 + 1)^{1}

(n + 4)^{3}

16 n^{2} + 22 n - 3

8 \frac{2}{8} - 3 \frac{3}{8}

\frac{7 \cdot b ^{5}}{b ^{4}}