Question

Rationalisation of denominator
$\frac{5 \sqrt{3} + \sqrt{2} }{4 \sqrt{5} }$
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Answer 1

Required Answer:-

Rationalizing the denominator means converting the denominator into a rational number, no matter what equivalent changes is made in the numerator.

Given fraction:

$\Large{\frac{5 \sqrt{3} + \sqrt{2} }{4 \sqrt{5} } }$

Here,

• The denominator is $4\sqrt{5}$.
• To change it into a rational number, we need to multiply √5 in both numerator and denominator.

Note:- We have chosen the least surd i.e. √5 to change it into the simplest form.

Multiplying √5 in both num. and den.

$\Large{= \frac{(5 \sqrt{3} + \sqrt{2} )( \sqrt{5} )}{4 \sqrt{5} \times \sqrt{5} } }$

$\Large{= \frac{5 \sqrt{15} + \sqrt{10} }{4 \times 5}}$

$\Large{ = \frac{5 \sqrt{15} + \sqrt{10} }{20}}$

Now the denominator is a rational number i.e. 20. Hence, rationalized!!

Answer 2

Step-by-step explanation:

PLEASE REFER TO THE ATTACHMENT.

REGARDS

dipankarroykiet