Question

rationalise root 10-root 5/root2​

Answer 1

√10 - √5 / √2 multiplying both number and denominator by √2 √2 ( √10 - √5 ) / √2 × √2 √20 - √10 / 2 2√5 - √10 / 2 Thus , answer 2√5 - √10 / 2 .

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Answer 2

Answer:

$\frac{2\sqrt{5} - \sqrt{10} }{2}$ is the required value of $\frac{\sqrt{10} - \sqrt{5} }{\sqrt{2} }$

Step-by-step explanation:

Explanation:

Given in the question, $\frac{\sqrt{10} - \sqrt{5} }{\sqrt{2} }$

• Rationalization - An irrational numberationalizedlised, or changed into a number that can be stated as the ratio of two integers, through the process of rationalization.

For rationalization:

• Therefore, we must remove all radicals from the denominator in order to justify it.

• In order to eliminate the radical in the denominator, multiply the numerator and denominator by the radical.

• Ensure that all radicals are condensed.

• If necessary, simplify the fraction.

Step 1:

We have, $\frac{\sqrt{10} - \sqrt{5} }{\sqrt{2} }$.

For rationalization, we need to multiply both numerator and denominator by $\sqrt{2}$.

⇒ $\frac{\sqrt{10} - \sqrt{5} }{\sqrt{2} }$ × $\frac{\sqrt{2} }{\sqrt{2} }$ = $\frac{\sqrt{20} - \sqrt{10} }{2}$.

Where $\sqrt{20}$ can be written as $2\sqrt{5}$.

⇒ $\frac{2\sqrt{5} - \sqrt{10} }{2}$

Final answer:

Hence, $\frac{2\sqrt{5} - \sqrt{10} }{2}$  is the required value of   $\frac{\sqrt{10} - \sqrt{5} }{\sqrt{2} }$.

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