Question

Rationalise the 5 / root 5 subtract root 3

Answer 1

The value of the expression is $\frac{5}{2}({\sqrt{5}+\sqrt{3}})$.

Step-by-step explanation:

The expression is:

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

Rationalise the denominator as follows:

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

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

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

Thus, the value of the expression is $\frac{5}{2}({\sqrt{5}+\sqrt{3}})$.

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