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

The solution to 1/((3-sqrt(2))^2) is 1/(11-6sqrt(2))

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

simplify

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

\frac{1}{11 - 6 2}

Decimal Notation

0.39765 \dots

Solution steps

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

Apply Perfect Square Formula:

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

(3 - 2)^{2} = 3^{2} - 2 \cdot 32 + (2)^{2}

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

3^{2} - 2 \cdot 32 + (2)^{2} = 11 - 62

= \frac{1}{11 - 6 2}

(5 n - 2 m) \cdot (5 n + 2 m)

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

\frac{6}{7} - \frac{9}{28}

(5 x^{2} + y)^{2}

\frac{5}{12} - \frac{- 16}{- 12}

What is 1/((3-sqrt(2))^2) ?
The solution to 1/((3-sqrt(2))^2) is 1/(11-6sqrt(2))