Question

rationalize the denominator 1 + root 2 upon 2 minus root 2​

Answer 1

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Answer 2

$\frac{1+\sqrt2}{2-\sqrt2}=\frac{4+3\sqrt2}{2}$

Step-by-step explanation:

Given : Expression $\frac{1+\sqrt2}{2-\sqrt2}$

To find : Rationalize the denominator of expression ?

Solution :

$\frac{1+\sqrt2}{2-\sqrt2}$

Rationalize the denominator,

$=\frac{1+\sqrt2}{2-\sqrt2}\times \frac{2+\sqrt2}{2+\sqrt2}$

$=\frac{2+\sqrt2+2\sqrt2+2}{2^2-(\sqrt2)^2}$

$=\frac{4+3\sqrt2}{4-2}$

$=\frac{4+3\sqrt2}{2}$

Therefore, $\frac{1+\sqrt2}{2-\sqrt2}=\frac{4+3\sqrt2}{2}$

#Learn more

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