Question

2] Rationalize the denominator
1)
$\frac{3}{2 \sqrt{5 } - 3 \sqrt{2} }$
please help me to solve thi question
form std :- 9th
math part 1 lesson 2 practice set 2.4


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Answer 1

please check the attachment

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Answer 2

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

Given :

$\sf = \frac{3}{2 \sqrt{5 } - 3 \sqrt{2} }$

To find :

Solution after Rationalisation of denominator

Solution :

$\sf = \frac{3}{2 \sqrt{5} - 3 \sqrt{2} }$

Step 1 : to rationalise denominator multiply and divide 2√5 + 3√2 to the term.

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

Step 2 : Multiply terms in denominator as well as numerator

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

Step 3 : Simplifying term by using formula

$\fbox{Formula to be used :}$

$\sf\bold\purple{:⟶ (x + y)(x - y) = {x}^{2} - {y}^{2} }$

$\sf = \frac{6 \sqrt{5} + 9\sqrt{2} }{ {(2 \sqrt{5} )}^{2} - {(3 \sqrt{2}) }^{2} }$

Step 4 : Simplifying by solving squares

$\sf = \frac{6 \sqrt{5} + 9 \sqrt{2} }{ {(2)}^{2} (\sqrt{5}) {}^{2} - {(3)}^{2} ( \sqrt{2}) {}^{2} }$

Step 5 : Solving denominator

$\sf = \frac{6 \sqrt{5} + 9 \sqrt{2} }{4 \times 5 - 9 \times 2}$

$\sf = \frac{6 \sqrt{5} + 9 \sqrt{2} }{20 - 18}$

$\sf = \frac{6 \sqrt{5} + 9 \sqrt{2} }{2}$

$or$

$\sf\huge\purple{ \frac{6 \sqrt{5} }{2} + \frac{9 \sqrt{2} }{2}}$