√(3 2√(2)) =√(2+1 2√(2)) Converting into (a b)^2 = a^2 + b^2 2ab =√((√(2))^2 + (1)^2 2 ×√(2)× 1) =√((√(2) 1)^2)=√(2) 1 ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Identities for Irrational Numbers

Simplify : √3...

Question

Simplify : $\sqrt{3 - 2 \sqrt{2}}$ .

Open in App

Solution

$\sqrt{3 - 2 \sqrt{2}}$

$= \sqrt{2 + 1 - 2 \sqrt{2}}$

$C o n v e r t i n g i n t o (a - b)^{2} = a^{2} + b^{2} - 2 a b$

$= \sqrt{(\sqrt{2})^{2} + (1)^{2} - 2 \times \sqrt{2} \times 1}$

$= \sqrt{(\sqrt{2} - 1)^{2}} = \sqrt{2} - 1$

Suggest Corrections

177

Similar questions

\frac{\sqrt{3} + \sqrt{2}}{\sqrt{3} - \sqrt{2}} + \frac{\sqrt{3} - \sqrt{2}}{\sqrt{3} + \sqrt{2}}

\frac{2 + \sqrt{3}}{\sqrt{2} + \sqrt{2 + \sqrt{3}}} + \frac{2 - \sqrt{3}}{\sqrt{2} - \sqrt{2 - \sqrt{3}}}

\sqrt{3} + \sqrt{2}

\times

\sqrt{3} - \sqrt{2}

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

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

Join BYJU'S Learning Program