What is rationalize 1/(5+sqrt(2)) ?

The solution to rationalize 1/(5+sqrt(2)) is (5-sqrt(2))/(23)

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rationalize 1/(5+sqrt(2))

rationalize

\frac{1}{5 + 2}

\frac{5 - 2}{23}

Decimal

0.15590 \dots

Solution steps

\frac{1}{5 + 2}

Multiply by the conjugate

\frac{5 - 2}{5 - 2}

= \frac{1 \cdot ( 5 - 2 )}{( 5 + 2 ) ( 5 - 2 )}

1 \cdot (5 - 2) = 5 - 2

(5 + 2) (5 - 2) = 23

= \frac{5 - 2}{23}

2 \times \frac{1}{2}

x^{2} - 3 x - 10

x + 1 - 2 x

\frac{3}{6 + i}

+ x^{3} + 7 x^{2} - 9 x - 63

What is rationalize 1/(5+sqrt(2)) ?
The solution to rationalize 1/(5+sqrt(2)) is (5-sqrt(2))/(23)