Nine Standard >> Radicals or surds | Introduction

A number in an 'exponential form' with a fractional index is called the root of a number.

Ex:- Square root of a is \(\sqrt{a}\) or \(a^{\frac{1}{2}}\)
       Cube root of b is \(\sqrt[3]{b}\) or \(b^{\frac{1}{2}}\)

Find the nth root of a number
If \(a=(x\times x\times x\times .......n \ times)(y\times y\times y\times .......n \ times)\)

\(\sqrt[n]{a}=\sqrt[n]{(x\times x\times x\times .......n\ times)(y\times y\times y\times .......n \ times)}\)

\(\sqrt[3]{64}=\sqrt[3]{(2\times2\times2)(2\times2\times2)}\)
                 \(=\sqrt[3]{2^{3}\times 2^{3}}\)
                 \(=\sqrt[3]{4^{3}}=4\)

\(\sqrt[3]{1728}=\sqrt[3]{(2\times2\times2)(2\times2\times2)}\)
                 \(=\sqrt[3]{2^{3}\times 2^{3} \times 3^{3}}\)
                    \(=2 \times 2 \times3=12\)