If m - 1-3-2-2 then- m2 - -

M = 1/3 2√(2) m = 1/3 2√(2)×3+2√(2)/3+2√(2) =3+2√(2)/(3)^2 (2√(2))^2 =3+2√(2)/9 8 =3+2√(2) m^2 = (3+2√(2))^2 =(3)^2+2(3)(2√(2))+(2√(2))^2 =9+12√(2)+8 =1 ...

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Byju's Answer

Standard VIII

Mathematics

Finding Square Root through Prime Factorisation

If m = 1/3-2√...

Question

$If m = \frac{1}{3 - 2 \sqrt{2}} then, m^{2} =$ _______.

$17 + 12 \sqrt{2}$

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$17 - 12 \sqrt{2}$

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$24 \sqrt{2}$

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$34$

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Solution

The correct option is A
$17 + 12 \sqrt{2}$

$m = \frac{1}{3 - 2 \sqrt{2}}$

$m = \frac{1}{3 - 2 \sqrt{2}} \times \frac{3 + 2 \sqrt{2}}{3 + 2 \sqrt{2}}$

$= \frac{3 + 2 \sqrt{2}}{(3)^{2} - (2 \sqrt{2})^{2}}$

$= \frac{3 + 2 \sqrt{2}}{9 - 8}$

$= 3 + 2 \sqrt{2}$

$m^{2} = (3 + 2 \sqrt{2})^{2}$

$= (3)^{2} + 2 (3) (2 \sqrt{2}) + (2 \sqrt{2})^{2}$

$= 9 + 12 \sqrt{2} + 8$

$= 17 + 12 \sqrt{2}$

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If m=13−2√2 then,m2= _______.

The correct option is A 17+12√2 m=13−2√2 m=13−2√2×3+2√23+2√2 =3+2√2(3)2−(2√2)2 =3+2√29−8 =3+2√2 m2=(3+2√2)2 =(3)2+2(3)(2√2)+(2√2)2 =9+12√2+8 =17+12√2

$If m = \frac{1}{3 - 2 \sqrt{2}} then, m^{2} =$ _______.