What is 1/((2+sqrt(3))^2) ?

The solution to 1/((2+sqrt(3))^2) is 1/(7+4sqrt(3))

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simplify 1/((2+sqrt(3))^2)

simplify

\frac{1}{( 2 + 3 ) ^{2}}

\frac{1}{7 + 4 3}

Decimal Notation

0.07179 \dots

Solution steps

\frac{1}{( 2 + 3 ) ^{2}}

Apply Perfect Square Formula:

(a + b)^{2} = a^{2} + 2 ab + b^{2}

(2 + 3)^{2} = 2^{2} + 2 \cdot 23 + (3)^{2}

= \frac{1}{2 ^{2} + 2 \cdot 2 3 + ( 3 ) ^{2}}

2^{2} + 2 \cdot 23 + (3)^{2} = 7 + 43

= \frac{1}{7 + 4 3}

- \frac{3}{4} + \frac{2}{3}

\frac{9 - 4 i}{i}

8 (x + 10)

8 (x^{2} + 2 x - 5) - 3 (2 x^{2} - 4 x + 3)

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