Question

these 2 Questions please
(root3-root5)square​

Answer 1

Question (vii) :- ${( \sqrt{3} - \sqrt{5})}^{2}$

Solution :-

$→ {( \sqrt{3} - \sqrt{5})}^{2}$

$→ {(\sqrt{3})}^{2} + {(\sqrt{5})}^{2} + 2( \sqrt{3})( \sqrt{5})$

$→3 + 5 + 2 \sqrt{15}$

$→8 + 2 \sqrt{15}$

Question (ix) :- $\frac{3}{ \sqrt{8} } + \frac{1}{ \sqrt{2} }$

Solution :-

$→ \frac{3}{ \sqrt{8} } + \frac{1}{ \sqrt{2} }$

$→ \frac{3}{2\sqrt{2}} + \frac{1}{\sqrt{2}}$

Rationalizing the terms,

$→ \frac{3}{2\sqrt{2}} \times \frac{2 \sqrt{2} }{2 \sqrt{2} } + \frac{1}{\sqrt{2}} \times \frac{ \sqrt{2} }{ \sqrt{2}}$

$→ \frac{6 \sqrt{2}}{4 \times 2} + \frac{ \sqrt{2} }{2}$

$→ \frac{ \cancel{6} \sqrt{2}}{ \cancel{8}} + \frac{ \sqrt{2} }{2}$

$→ \frac{3 \sqrt{2}}{4} + \frac{ \sqrt{2} }{2}$

$→ \frac{3 \sqrt{2} + 2 \sqrt{2}}{4}$

$→ \frac{5 \sqrt{2} }{4}$