Question

simplify root 3 ( root 15 - root 60

Answer 1

Solution :

3√15 - √60

= 3√15 - √ [( 2×2 )× 15]

= 3√15 - 2√15

= (3 - 2)√15

= √15

••••

Answer 2

Identity used :

$\boxed{\mathbf{\sqrt{{a}^{2}} = a}}$

$\underline{\underline{\huge\mathfrak{Solution}}}$

$\sqrt{3} ( \sqrt{15} - \sqrt{60} )$

The Prime factorization of 60 is 2² × 3 × 5 i.e. 60 can also be written as 2² × 3 × 5

$= \sqrt{3} ( \sqrt{15} - \sqrt{ {2}^{2} \times 3 \times 5 } ) \\ \\ = \sqrt{3} ( \sqrt{15} - 2 \sqrt{15} ) \\ \\ = \sqrt{3} ( - \sqrt{15} ) \\ \\ \bf 15 \: can \: also \: be \: written \: as \: 3 \times 5 \\ \\ = \sqrt{3} \times - \sqrt{3 \times 5} \\ \\ \bf = - 3 \sqrt{5}$