Question

Rationalise the denominator:
1.) 1/3 under root 6
2.) 5 under root 3/under root 5

Answer 1

Answer: Step-by-step explanation:

1 ) : $\dfrac{1}{3\sqrt{6}}$

As we have to rationalize the denominator, we will have to multiply the root of term which is under the root, or to make the square or to remove square root from the term. Here, that term is √6.

And thus, multiplying by √6 on denominator and numerator both

= > $\dfrac{1}{3\sqrt{6}}\times \dfrac{\sqrt{6}}{\sqrt{6}}$

= > $\dfrac{\sqrt{6}}{3 (\sqrt{6})^2}$

= > $\dfrac{\sqrt{6}}{3\times 6}$

= > $\dfrac{\sqrt{6}}{18}$

2 ) : $\dfrac{5\sqrt{3}}{\sqrt{5}}$

As we have to rationalize the denominator, we will have to multiply the root of term which is under the root, or to make the square or to remove square root from the term. Here, that term is √5.

And thus, multiplying by √5 on denominator and numerator both

= > $\dfrac{5\sqrt{3}}{\sqrt{5}}\times \dfrac{\sqrt{5}}{\sqrt{5}}$

= > $\dfrac{5\sqrt{3}\times\sqrt{5}}{ (\sqrt{5})^2}$

= > $\dfrac{5\sqrt{15}}{5}$

= > √15