Question

rationalize the denominator​

Answer 1

$\sf\dfrac{3 \sqrt{5} - \sqrt{7} }{3 \sqrt{3} + \sqrt{2} }$

Given to rationalize

For rationalising denominator Radical of denominator must be removed So, multiply and divide with its rationalizing factor

Rationalizing factor of

$\3 \sqrt{3} + \sqrt{2} \: \: is \: 3 \sqrt{3} - \sqrt{2}$

Multiply and divide with its

So,

$\sf\dfrac{3 \sqrt{5} - \sqrt{7} }{3 \sqrt{3} + \sqrt{2} } \times \frac{3 \sqrt{3 } - \sqrt{2} }{3 \sqrt{3} - \sqrt{2} }$

$\sf\dfrac{3√5(3√3-√2)-√7(3√3-√2}{(3√3)²-(√2)²}$

$\sf\dfrac{9 \sqrt{15} - 3 \sqrt{10} }{27 - 2}$

$\sf\dfrac{9 \sqrt{15} - 3 \sqrt{10}$-3$\sf\sqrt{21}$-$\sf\sqrt{14}$}{25} [/tex]

Hence denominator rationalized

Used identity for rationalizing denominator

(a+b)(a-b) = a²-b²

If u confused with latex Once plz refer attachment for easy understanding