Question

write the above surd in simplest form write with full explanation please ​

Answer 1

$\frac{3}{4} \sqrt{8} = \frac{3}{4} 2 \sqrt{2} = \frac{3}{2} \sqrt{2} = \frac{3 \sqrt{2} }{2} = \frac{3}{ \sqrt{2} }$

Answer 2

$\dfrac{3 \sqrt{2} }{2}$

Step-by-step explanation:

Simplest Form ?

1. Just Break the surd in small factors.

$\sqrt{8} = \sqrt{2 \times 2 \times 2} \\ \\ = 2 \sqrt{2}$

2. Simplify it's mean cut the factors,

$=\frac{3}{4} \sqrt{8} \\ \\ = \frac{3}{2 \times 2} \times 2 \sqrt{2} \\ \\ = \frac{3}{ \cancel{2}\times 2} \times \cancel{2} \sqrt{2} \\ \\ = \frac{3 \sqrt{2} }{2}$

We further Simplify it,

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

But, Denominator is not written in surd form.

$\therefore \textsf{Our Answer is} = \boxed{ \frac{3 \sqrt{2} }{2} }$