To calculate the square root of a number using indices (also known as exponents), you can express the square root operation by raising the number to the power of $\frac{1}{2}$.

For instance, if you want to find the square root of $16$, you can write it as:

This representation is valid because the square root of a number is equivalent to raising that number to the exponent $0.5$.

Let’s delve deeper into the concept of indices. Indices are a method of expressing repeated multiplication. For example, the expression $2^3$ means $2$ multiplied by itself three times, which can be written as:

When you are finding the square root, you are essentially identifying a number that, when multiplied by itself, results in the original number. By using the exponent $\frac{1}{2}$, you are specifying that you want the number which, when squared, equals the original number.

Take the number $25$ as an example. To determine its square root using indices, you would express it as:

Since $5 \times 5 = 25$, we conclude that the square root of $25$ is $5$. Therefore, we can write:

This method is applicable to any positive number. If you have a calculator that supports exponentiation, you can easily compute the square root by entering the number followed by the exponent $0.5$. For example, to find the square root of $81$, you would input:

This operation yields $9$, since $9 \times 9 = 81$.

Utilizing indices to find square roots is a powerful approach, particularly when dealing with more complex numbers or when a quick and accurate calculation is required.