Question

Solve this question and simplify:-

Answer 1

Answer :-

Option- D

Given to find the value of :-

$\sqrt{5 \sqrt{2} - 2 \sqrt{12} }$

SOLUTION :-

$\sqrt{12} \: can \: be \: written \: as \: \sqrt{2} \times \sqrt{6}$

$= \sqrt{5 \sqrt{2} - 2 \sqrt{6} \sqrt{2} }$

Now , take common √2

$= \: \sqrt{ \sqrt{2}(5 - 2 \sqrt{6}) }$

Now 5-2√6 can be written as in terms of square of a number i.e finding the square root

$= \sqrt{ \sqrt{2}( 3 + 2 - 2 \sqrt{2} \sqrt{6} ) }$

$= \sqrt{ \sqrt{2}(( \sqrt{3}) {}^{2} + ( \sqrt{2} ) {}^{2} - 2 \sqrt{3} \sqrt{2} ) }$

i.e it is in form of (a-b)² = a² -2ab + b²

$= \sqrt{ \sqrt{2}( \sqrt{3} - \sqrt{2}) {}^{2} }$

$= \sqrt{ \sqrt{2} } \times \sqrt{( \sqrt{3} - \sqrt{2} ) {}^{2} }$

$= \sqrt{ \sqrt{2} } ( \sqrt{3} - \sqrt{2})$

$\sqrt{2 {}^{ \frac{1}{2} } } ( \sqrt{3} - \sqrt{2} )$

$= 2 {}^{ \frac{1}{2} \times \frac{1}{2} } (\sqrt{3} - \sqrt{2} )$

$= 2 {}^{ \frac{1}{4} } ( \sqrt{3} - \sqrt{2} )$

$\sqrt[4]{2} ( \sqrt{3} - \sqrt{2} )$

So, the correct option is D

Answer 2

Answer :-

Option- D

Given to find the value of :-

$\sqrt{5 \sqrt{2} - 2 \sqrt{12} }$

SOLUTION :-

$\sqrt{12} \: can \: be \: written \: as \: \sqrt{2} \times \sqrt{6}$

$= \sqrt{5 \sqrt{2} - 2 \sqrt{6} \sqrt{2} }$

Now , take common √2

$= \: \sqrt{ \sqrt{2}(5 - 2 \sqrt{6}) }$

Now 5-2√6 can be written as in terms of square of a number i.e finding the square root

$= \sqrt{ \sqrt{2}( 3 + 2 - 2 \sqrt{2} \sqrt{6} ) }$

$= \sqrt{ \sqrt{2}(( \sqrt{3}) {}^{2} + ( \sqrt{2} ) {}^{2} - 2 \sqrt{3} \sqrt{2} ) }$

i.e it is in form of (a-b)² = a² -2ab + b²

$= \sqrt{ \sqrt{2}( \sqrt{3} - \sqrt{2}) {}^{2} }$

$= \sqrt{ \sqrt{2} } \times \sqrt{( \sqrt{3} - \sqrt{2} ) {}^{2} }$

$= \sqrt{ \sqrt{2} } ( \sqrt{3} - \sqrt{2})$

$\sqrt{2 {}^{ \frac{1}{2} } } ( \sqrt{3} - \sqrt{2} )$

$= 2 {}^{ \frac{1}{2} \times \frac{1}{2} } (\sqrt{3} - \sqrt{2} )$

$= 2 {}^{ \frac{1}{4} } ( \sqrt{3} - \sqrt{2} )$

$\sqrt[4]{2} ( \sqrt{3} - \sqrt{2} )$

So, the correct option is D