Question

it being given that √2=1.414,√3=1.732,√5=2.236 and √10=3.162, find the value to three places of decimals of each of the following

1) 2/√5

2) 2-√3/√3

3) √10-√5/√2

help box(answer), 1) 0.894
2) 0.155
3),0.655
​ please tell me explanation

Answer 1

Answer:

The given expressions are evaluated after rationalizing its denominators.

Given:

$\sqrt2=1.414,\sqrt3=1.732,\sqrt5=2.236\:and\:\sqrt{10}=3.162$

1.

$\frac{2}{\sqrt5}$

$=\frac{2}{\sqrt5}*\frac{\sqrt5}{\sqrt5}$

$=\frac{2\sqrt5}{5}$

$=\frac{2(2.236)}{5}$

$=\frac{4.472}{5}$

$=0.8945$

2.

$\frac{2-\sqrt3}{\sqrt3}$

$=\frac{2-\sqrt3}{\sqrt3}*\frac{\sqrt3}{\sqrt3}$

$=\frac{2\sqrt3-3}{3}$

$=\frac{2(1.732)-3}{3}$

$=\frac{3.464-3}{3}$

$=\frac{0.464}{3}$

$=0.1546$

3.

$\frac{\sqrt{10}-\sqrt5}{\sqrt2}$

$=\frac{\sqrt{10}-\sqrt5}{\sqrt2}*\frac{\sqrt2}{\sqrt2}$

$=\frac{\sqrt{20}-\sqrt{10}}{2}$

$=\frac{2\sqrt{5}-\sqrt{10}}{2}$

$=\frac{2(2.236)-3.162}{2}$

$=\frac{4.472-3.162}{2}$

$=\frac{1.310}{2}$

$=0.655$

Answer 2

Explanation:

here , given : √2=1.414,√3=1.732,√5=2.236 and √10=3.162

(i)

$\frac{2}{\sqrt{5}}\\\\rationalising\\\\\frac{2}{\sqrt{5}}\times \frac{\sqrt{5}}{\sqrt{5}}\\\\\frac{2\sqrt{5}}{5}\\\\\frac{2\times 2.236}{5}\\\\\frac{4.472}{5}\\\\= 0.8945$

$(ii)\frac{2-\sqrt{3}}{\sqrt{3}}\\\\rationalizing\\\\\frac{2-\sqrt{3}}{\sqrt{3}}\times \frac{\sqrt{3}}{\sqrt{3}}\\\\\frac{2\sqrt{3}-3}{3}\\\\\frac{2\times1.732-3)}{3}\\\\\frac{0.464}{3}\\\\=0.1546\sim 0.1555$

$(iii)\frac{\sqrt{10}-\sqrt{5}}{\sqrt{2}}\\\\rationalizing\\\\\frac{\sqrt{10}-\sqrt{5}}{\sqrt{2}}\times\frac{\sqrt{2}}{\sqrt{2}} \\\\\frac{2\sqrt{5}-\sqrt{10}}{2}\\\\\frac{2(2.236)-(3.162)}{2}\\\\\frac{4.472-3.162}{2}\\\\\frac{1.310}{2}\\\\=0.655$

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