Question

root 10- root 5 /2root2

Answer 1

Hey friend,
Here is the answer you were looking for:
$\frac{ \sqrt{10} - \sqrt{5} }{2 \sqrt{2} }$

On rationalizing the denominator we get,

$= \frac{ \sqrt{10} - \sqrt{5} }{2 \sqrt{2} } \times \frac{2 \sqrt{2} }{2 \sqrt{2} } \\ \\ = \frac{2 \sqrt{2}( \sqrt{10} - \sqrt{5} ) }{ {(2 \sqrt{2}) }^{2} } \\ \\ = \frac{2 \sqrt{20} - 2 \sqrt{10} }{8} \\ \\ = \frac{ 2\sqrt{2 \times 2 \times 5} - 2 \sqrt{10} }{8} \\ \\ = \frac{2 \times 2 \sqrt{5} - 2 \sqrt{10} }{8} \\ \\ = \frac{4 \sqrt{5} - 2 \sqrt{10} }{8} \\ \\ = \frac{2 \sqrt{5} - \sqrt{10} }{4}$

This can be the answer but if you want, you can solve more...
Lemme do that solve as well ^_^

We know that √5 = 2.236
√10 == 3.162

So, putting the value :

$= \frac{2 \times 2.236 - 3.162}{4} \\ \\ = \frac{4.472 - 3.162}{4} \\ \\ = \frac{1.31}{4} \\ \\ = 0.327 \: (approx)$

Hope this helps!!

If you have any doubt regarding to my answer, feel free to ask in the comment section or inbox me if needed.

@Mahak24

Thanks...
☺☺