Question

brainly me hai koi meri madat karne wala​

Answer 1

Answer:

Value is 3√6

Step-by-step explanation:

Given :-

$\bold{\mathsf{= \frac{1}{2} \sqrt{486} - \sqrt{ \frac{27}{2} }}}$

Make prime factors of 486 and 27 as done below

$= \frac{1}{2} \sqrt{486} - \sqrt{ \frac{27}{2} } \\ \\ = \frac{1}{2} \times 9 \sqrt{6} - \frac{3 \sqrt{3} }{\sqrt{2} } \\ \\ = \frac{9 \sqrt{3} \sqrt{2} }{ \sqrt{2} \times \sqrt{2} } - \frac{3 \sqrt{3} }{ \sqrt{2} } \\ \\ = \frac{9 \sqrt{3} - 3 \sqrt{3} }{ \sqrt{2} } \\ \\ = \frac{6 \sqrt{3} }{ \sqrt{2} }$

Now by rationalizing the final term

$= \frac{6 \sqrt{3} }{ \sqrt{2} } \times \frac{ \sqrt{2} }{ \sqrt{2} } \\ \\ = \frac{6 \sqrt{6} }{2} \\ \\ = 3 \sqrt{6}$

$\rule{200}{1}$

Rules to know:

• √x × √x = x

• (√x)² = x