Question

Evaluate $\dfrac{15}{\sqrt{10} + \sqrt{20} + \sqrt{40} - \sqrt{5} - \sqrt{80}}$, it being given that $\sqrt{5} = 2.236$ and $\sqrt{10} = 3.162$

HINT : $\begin {aligned} \dfrac{15}{\sqrt{10} + \sqrt{20} + \sqrt{40} - \sqrt{5} - \sqrt{80}} & = \dfrac{15}{\sqrt{10} + 2\sqrt{5} + 2\sqrt{10} - \sqrt{5} - 4\sqrt{5}} \\\\& = \dfrac{15}{3\sqrt{10} - 3\sqrt{5}} = \dfrac{5}{\sqrt{10} - \sqrt{5}} \end {aligned}$

Answer 1

Step-by-step explanation:

जीवमंडल तापमान, भौगोलिक संदर्भ आदि पर निर्भर करता है। निर्मित पर्यावरण में मानव शामिल है

Answer 2

Required Answer:-

Given To Evaluate:

• $\dfrac{15}{\sqrt{10} + \sqrt{20} + \sqrt{40} - \sqrt{5} - \sqrt{80}}$

Solution:

Given,

$= \dfrac{15}{\sqrt{10} + \sqrt{20} + \sqrt{40} - \sqrt{5} - \sqrt{80}}$

This can be written as,

$= \dfrac{15}{\sqrt{10} + \sqrt{4 \times 5} + \sqrt{4 \times 10} - \sqrt{5} - \sqrt{16 \times 5}}$

Square root of 4 is 2 and 16 is 4,

$= \dfrac{15}{\sqrt{10} + 2\sqrt{5} + 2\sqrt{10} - \sqrt{5} - 4\sqrt{5}}$

Simplify the denominator part,

$= \dfrac{15}{3\sqrt{10} - 3\sqrt{5} }$

Take 3 as common from the denominator,

$= \dfrac{15}{3(\sqrt{10} - \sqrt{5} )}$

$= \dfrac{5}{\sqrt{10} - \sqrt{5}}$

Again, take √5 as common from denominator,

$= \dfrac{5}{ \sqrt{5}( \sqrt{2} - 1)}$

$= \dfrac{ \sqrt{5} \times \sqrt{5} }{ \sqrt{5}( \sqrt{2} - 1)}$

$= \dfrac{\sqrt{5} }{\sqrt{2} - 1}$

Rationalise the denominator,

$= \dfrac{\sqrt{5} }{(\sqrt{2} - 1)} \times \dfrac{( \sqrt{2} + 1) }{( \sqrt{2} + 1)}$

$= \dfrac{\sqrt{5}( \sqrt{2} + 1) }{(\sqrt{2} - 1)( \sqrt{2} + 1)}$

$= \dfrac{\sqrt{5}( \sqrt{2} + 1) }{2 - 1}$

$= \sqrt{5}( \sqrt{2} + 1)$

$= \sqrt{10} + \sqrt{5}$

Putting the values of √10 and √5, we get,

$= 3.162 + 2.236$

$= 5.398$

★ Hence, the required answer is 5.398.

Answer:

• After evaluation, result - 5.398