Question

pls solve it and help me​ it is from (Rational and irrational numbers) chapter of class nine

Answer 1

Answer:

Rationalizing factor of root15 + 2root2 is root15 - 2root2

Answer 2

We rationalise a denominator by multiplying the fraction by its conjugate.

Here, conjugate of $\sf \sqrt{15} + 2 \sqrt{2} \; is \; \sqrt{15} - 2 \sqrt{2}$

$\sf \implies \dfrac{7}{ \sqrt{15} + 2 \sqrt{2} } \times \dfrac{ \sqrt{15} - 2 \sqrt{2}}{ \sqrt{15} - 2 \sqrt{2}} = \dfrac{7 \sqrt{15} - 14 \sqrt{2}}{ ( \sqrt{15} )^2 - (2 \sqrt{2} )^2 }$

$\sf \implies \dfrac{7 \sqrt{15} - 14 \sqrt{2}}{15 - 8} = \dfrac{ 7 \sqrt{15} - 14 \sqrt{2}}{7}$

$\implies \sf \dfrac{\cancel{7}( \sqrt{15} - 2 \sqrt{2} )}{\cancel{7}} =15 - 2 \sqrt{2}$

Answer:- $\bf 15 - 2 \sqrt{2}$