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Find the square root of $7 - 2 \sqrt{10}$

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\sqrt{15} - \sqrt{2}

\sqrt{3} - \sqrt{2}

\sqrt{5} - \sqrt{3}

\sqrt{5} - \sqrt{2}

answer is D.

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Detailed Solution

we have to find the

\sqrt{7 - 2 \sqrt{10}}

Now we can write the above expression as
⇒

\sqrt{7 - 2 \sqrt{2 . 5}}

As we know

\sqrt{ab} = \sqrt{a} \sqrt{b}

Therefore, on applying the above formula we get
⇒

\sqrt{7 - 2 \sqrt{5} \sqrt{2}}

Now on rewriting the7 as 5 + 2, we get
⇒

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

Now, as we know that a2−2ab+b2=(a−b)2
So on applying the formula and substituting the values, we get
⇒

\sqrt{{(\sqrt{5} - \sqrt{2})}^{2}}

Therefore, now on applying the rule

\sqrt{a^{2}} = | a |

, we get
⇒∣∣

(\sqrt{5} - \sqrt{2})

∣∣
And it can also be written as

(\sqrt{5} - \sqrt{2})

Therefore, the option (4) is correct.

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