Question

m=1/3-√8
find m2
Helpppp

Answer 1

Given:

$m = \frac{1}{3} - \sqrt{8}$

To Find:

Value of 'm²'

★Solution★

On simplifying the value of 'm';

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

$⇒m = \frac{1 - 6\sqrt{2} }{3}$

Now, For finding the value of its square,

On squaring both sides:

$(m) {}^{2} = ( \frac{1 - 6\sqrt{2} }{3} ) {}^{2}$

$m {}^{2} = ( \frac{1 - 6\sqrt{2} }{3} )( \frac{ 1 - 6 \sqrt{2} }{3} )$

$m {}^{2} = \frac{(1 - 6 \sqrt{2}) {}^{2} }{(3)(3)}$

$m {}^{2} = \frac{(1) {}^{2} - 2(1)(6 \sqrt{2} ) + (6 \sqrt{2} ) {}^{2} }{9}$

$m {}^{2} = \frac{1 + 72 - 12 \sqrt{2} }{9}$

$⇒m {}^{2} = \frac{73 - 12\sqrt{2} }{9}≈6.2255$