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

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

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

rationalize

\frac{1}{3 + 2}

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

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}

\frac{1}{3} \times \frac{1}{5}

5 27 x - 75 x

2 x^{2} + 72

(1 + 2 i) (4 + 3 i)

9 x^{4} - 4

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