Question

Please solve this quickly

Answer 1

√486 can be written as
√(2X3X3X3X3X3
so it can be written as 9√6
$\frac{9 \sqrt{6} }{2} - \sqrt{ \frac{27}{2} }$
$\frac{9 \sqrt{6} }{2} - \frac{3 \sqrt{3} }{ \sqrt{2} }$
$= \frac{9 \sqrt{6} \sqrt{2} - 6 \sqrt{3} }{2 \sqrt{2} } \\ \frac{9 \sqrt{12} - 6 \sqrt{3} }{2 \sqrt{2} }$
$= \frac{9 \times 2 \sqrt{3} - 6 \sqrt{3} }{2 \sqrt{2} } \\ = \frac{18 \sqrt{3} - 6 \sqrt{3} }{2 \sqrt{2} }$
$= \frac{12 \sqrt{3} }{2 \sqrt{2} } \\ = \frac{6 \sqrt{3} }{ \sqrt{2} }$
rationalize the denominator
$= \frac{6 \sqrt{3} \sqrt{2} }{ \sqrt{2} \sqrt{2} } \\ = \frac{6 \sqrt{6} }{2}$
$= 3 \sqrt{6}$
is the final answer

Answer 2

we can write this question as 1/2 √2×3×3×3×3×3 - √ 27 /2
=1/2×3×3√2×3. - √3×3×3 /2
=1/2×3×3√2×3- 3√3/2
=3×3√1/4×2×3-. 3√3/2
=9√3/2 - 3√3/2
=√3/2. (9-3)
√3/2. ×6
so the answer is 6√3/2