Question

How do you find two square roots of a number?

Answer 1

Hint: Given the numbers in the form of a radical expression. First, we will find the factors of the terms inside the radical. Then, write the result in a simplified form. Also, we will try to factor the radicand further. If the factors of the term are not possible, then the result in simplified form.

Complete step-by-step solution:
In any expression, there must exist two square roots of any positive real number ; one is the positive square root and another is the negative square root of that number.
This is possible because the multiplication of two positive or two negative numbers is always positive. For example, consider the number ${a^2} = 16$.
We will find the square root of the number by taking the square root at the both sides.
$ \Rightarrow a = \sqrt {16} $
Here, the number $16$ can be written as $4 \times 4$ and also $\left( { - 4} \right) \times \left( { - 4} \right)$
Therefore, the square root of the number $16$ can be written as:
$ \Rightarrow \pm \sqrt {16} = \pm 4$

Hence there exist two square roots of a number that is positive or negative.

Additional Information: The square root of the negative number is not possible because it will give the imaginary value and the square root of the real number is always in real form. The principal square root of a number is always a positive real number.

Note: In such types of questions students mainly get confused in applying the formula. As they don't know which formula they have to apply. So, when a certain number is given, then to find the square root of the number, then it is necessary to substitute the plus-minus sign before the radical symbol because the product of two negative and positive numbers is always positive.