What is 1/(sqrt(3+\sqrt{2))} ?

The solution to 1/(sqrt(3+\sqrt{2))} is ((3-sqrt(2))sqrt(3+\sqrt{2)})/7

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simplify 1/(sqrt(3+\sqrt{2))}

simplify

\frac{1}{3 + 2}

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

Decimal Notation

0.47596 \dots

Solution steps

\frac{1}{3 + 2}

Multiply by the conjugate

\frac{3 + 2}{3 + 2}

= \frac{1 \cdot 3 + 2}{3 + 2 3 + 2}

1 \cdot 3 + 2 = 3 + 2

3 + 2 3 + 2 = 3 + 2

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

Multiply by the conjugate

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

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

(3 + 2) (3 - 2) = 7

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

x^{8} \cdot x \cdot x^{5}

- 8 \times (- 8)

14 \times 8

2 - 50

\frac{5}{6} - \frac{3}{14}

What is 1/(sqrt(3+\sqrt{2))} ?
The solution to 1/(sqrt(3+\sqrt{2))} is ((3-sqrt(2))sqrt(3+\sqrt{2)})/7