Question

What is the square root of $a{{b}^{2}}$ ?

Answer 1

Hint: We know that the square root of a number is a value which on multiplication with itself gives the original number. Now suppose that x is the square root of y, then it is represented as $x=\sqrt{y}$ or we can also write it as ${{x}^{2}}=y$ . Here, the radical symbol is used to represent the root of the numbers.

Complete step-by-step solution:
The positive number when multiplied by itself then represents the square of a number. The square root of the square of a positive number gives the original number. In the case of the square root of a negative number we get a complex number.
Now, some properties of the square root of a number are:
1. If we have a perfect square number, then we will have the square root of that number.
2. If a number ends with an even number of zeros, then it can have a square root.
3. The two square root values can be multiplied.
4. When two same square roots are multiplied, then the result should be a radical number. It means that the result is a non-square root number.
5. The square root of any negative numbers is not defined. Because the perfect square cannot be negative.
Now in question we need to find the square root of $a{{b}^{2}}$
Which is $\sqrt{a{{b}^{2}}}=|b|\sqrt{a}$
This is our required result.

Note: In this question you may put plus and minus sign together in spite of putting modulus at b. We must be careful while writing the answer as missing signs or writing the answer with wrong plus minus symbols will make a major difference in logic behind it.