Question

Rationalise this
30/5√3-3√5=

Answer 1

Hey friend, Harish here.

Here is your answer:

To rationalize the expression:    

$\frac{30}{5 \sqrt{3} -3 \sqrt{5} }$

Solution:

To rationalize a number we must multiply and divide the number by it's conjugate.

Conjugate of denominator is  5√3 + 3√5.

Then,

$\frac{30}{5 \sqrt{3} -3 \sqrt{5} }= \frac{30}{5 \sqrt{3} -3 \sqrt{5} }\times \frac{5 \sqrt{3} +3 \sqrt{5}}{5 \sqrt{3} +3 \sqrt{5}}$

We know that,

$( a+b)(a-b) =a^{2}-b^{2}$

Using the identity to multiply the denominators , We get.

$(5 \sqrt{3} -3 \sqrt{5})(5 \sqrt{3} +3 \sqrt{5}) = (5 \sqrt{3})^{2} -(3 \sqrt{5})^{2} = 75 -45 = 30$

Then,

$\frac{30}{5 \sqrt{3} -3 \sqrt{5} }\times \frac{5 \sqrt{3} +3 \sqrt{5}}{5 \sqrt{3} +3 \sqrt{5}} = \frac{(30)(5 \sqrt{3} +3 \sqrt{5}) }{30} = \frac{5 \sqrt{3} -3 \sqrt{5} }{1} =5 \sqrt{3} -3 \sqrt{5}$

Hence the denominator is rationalized.
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Hope my answer is helpful to you.

Answer 2

Hey mate !!

Here's your answer !!

Refer to the attachment !!

Hope it helps !!

Cheers !!