Question

evaluate : root 5 + root 2 / root 5 - root 2 given that root 10 =3.162

Answer 1

Answer:

thankyou for your answer dear god bless you

Answer 2

The correct answer is 4.441.

Given: The equation = $\frac{\sqrt{5}+\sqrt{2} }{\sqrt{5}-\sqrt{2}}$.

To Find: Evaluate the equation.

Solution:

$\frac{\sqrt{5}+\sqrt{2} }{\sqrt{5}-\sqrt{2}}$

Rationalize the term.

=  $\frac{\sqrt{5}+\sqrt{2} }{\sqrt{5}-\sqrt{2}}*\frac{\sqrt{5}+\sqrt{2} }{\sqrt{5}+\sqrt{2}}$

=  $\frac{(\sqrt{5}+\sqrt{2}) ^{2} }{\sqrt{5}^{2} -\sqrt{2}^{2} }$

=  $\frac{(\sqrt{5}+\sqrt{2}) ^{2} }{5-2}$

=  $\frac{\sqrt{5}^{2} +\sqrt{2}^{2} +2\sqrt{5} \sqrt{2} }{3}$

=  $\frac{5+2 +2\sqrt{5} \sqrt{2} }{3}$

=  $\frac{7 +2\sqrt{10} }{3}$

As given in the question $\sqrt{10}=3.162$.

= $\frac{7+2(3.162)}{3}$

= $\frac{7+6.324}{3}$

= $\frac{13.324}{3}$

= 4.441

Hence, the answer is 4.441.

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