Question

Rationalise the dinominator 1/5-root 3

Answer 1

Question:-

Rationalize the denominators:-

$\bf \: \frac{1}{5 - \sqrt{3} }$

Solution:-

$\bf \: \frac{1}{5 - \sqrt{3} }$

Now multiply and divide by

$5 + \sqrt{3}$

We get ,

$\bf \: \frac{1}{5 - \sqrt{3} } \times \frac{5 + \sqrt{3} }{5 + \sqrt{3} }$

Using this identity

=> (a - b )(a + b )= a² - b²

$\bf \: \frac{5 + \sqrt{3} }{(5) {}^{2} - ( \sqrt{3} ) {}^{2} }$

$\bf \: \frac{5 + \sqrt{3} }{25 - 3}$

$\boxed{ \green{ \bf{ answer = \frac{5 + \sqrt{3} }{22} }}}$

Answer 2

AnswEr:-

Your Answer Is $\bf\dfrac{5+\sqrt{3}}{22}.$

ExplanaTion:-

Here we have to rationalize a denominator of $\dfrac{1}{5-\sqrt{3}}.$

So Let us first find out the meaning of "Rationalization."

$\large{\bf{\underline{\underline {Rationalization:-}}}}$

• Converting any irrational number to a rational by by using Suitable Identities is called Rationalization.

So Here,

We have to convert the denominator to a rational number.

ID Which we can use:-

$\bf\longrightarrow\boxed{\bf(a+b)(a-b) = a^2-b^2.}$

Now,

Lets Rationalize the denominator by using above ID:-

$\tt\mapsto\dfrac{1}{5 - \sqrt{3}}.$

$\tt = \bigg(\dfrac{1}{5 - \sqrt{3}} \bigg) \times \bigg ( \dfrac{5 + \sqrt{3} }{5 + \sqrt{3} } \bigg).$

$\tt = \dfrac{1 \times (5 + \sqrt{3)} }{(5 + \sqrt{3}) \times (5 - \sqrt{3} )} .$

$\tt = \dfrac{5 + \sqrt{3} }{(5 + \sqrt{3})(5 - \sqrt{3}) } .$

$\tt = \dfrac{5 + \sqrt{ 3 } }{(5) {}^{2} - ( \sqrt{3}) {}^{2} } .$

$\tt = \dfrac{5 + \sqrt{3} }{25 - (\sqrt{3} \times \sqrt{3}) } .$

$\tt = \dfrac{5 + \sqrt{3} }{25 - 3} .$

$\bf\boxed{ = \dfrac{5 + \sqrt{3} }{22} .}$