Question

simplify (root5-root2)(root2-root3)​

Answer 1

Answer:

$\large{\text{ \mathrm{\sqrt{6} +\sqrt{10}-2 -\sqrt{15} } }}$

Step-by-step explanation:

Given Question :

$\mathrm{(\sqrt{5}- \sqrt{2})( \sqrt{2}- \sqrt{3} )}$

To find :

Simplification the given expression

Solution :

$\longmapsto \mathrm{(\sqrt{5}- \sqrt{2})( \sqrt{2}- \sqrt{3} )}$

$\implies \mathrm{\big(\sqrt{5}( \sqrt{2}- \sqrt{3} )- \sqrt{2}( \sqrt{2}- \sqrt{3} )\big)}$

$\implies \mathrm{(\sqrt{10}- \sqrt{15}- \sqrt{4} +\sqrt{6} )}$

$\implies \mathrm{\sqrt{6} +\sqrt{10}-2 -\sqrt{15} }$

$\therefore \underline{\boxed{\mathbf{(\sqrt{5}- \sqrt{2})( \sqrt{2}- \sqrt{3} )} =\mathbf{\sqrt{6} +\sqrt{10}-2 -\sqrt{15} } }}$

Hope it helps!!

Answer 2

$\sf\huge\bold{Answer:}$

Given :

$\sf = (\sqrt{5} - \sqrt{2} )( \sqrt{2} - \sqrt{3} )$

To find :

Value of above expression on simplification

Solution :

$\sf = ( \sqrt{5} - \sqrt{2} )( \sqrt{2} - \sqrt{3} )$

$\sf = \sqrt{5} ( \sqrt{2} - \sqrt{3} ) - \sqrt{2} ( \sqrt{2} - \sqrt{3} )$

$\sf = \sqrt{5 \times 2} - \sqrt{5 \times 3} - \sqrt{2 \times 2} - ( - \sqrt{2 \times 3} )$

$\sf = \sqrt{10} - \sqrt{15} - \sqrt{4} + \sqrt{6}$

$\sf = \sqrt{10} - \sqrt{15} - \sqrt{{2}^{2} } + \sqrt{6}$

$\sf = \sqrt{10} - \sqrt{15} - 2 + \sqrt{6}$

$\sf = \sqrt{6} + \sqrt{10} - \sqrt{15} - 2$

$\sf\huge\purple{ :⟶ (\sqrt{5} - \sqrt{2} )( \sqrt{2} - \sqrt{3} )}$

$\sf\huge\purple{ = \sqrt{6} + \sqrt{10} - \sqrt{15} - 2 }$