# Square Roots: Definition with Solved Problems

The square root is one of the main topics in Mathematics. This page includes simplifications of many square roots in their simplest radical forms.

## Definition of Square Root

If two numbers x and d satisfy the following equation

x2 = d,

then the number x is called a square root of the number d. Symbolically, we write it as follows

x=√d.

For example, we have 72 = 49, so from the above definition of square roots we can conclude that 7 is a square root of 49.

## Properties of Square Roots

Square roots have the following properties:

• The square root of zero is always zero.
• A square root of a number can be positive or negative. For example, 5 and -5 are square roots of 25.
• Two square roots can be multiplied as follows √a × √b = √(ab).
• Division rule for square roots: √a ÷ √b = √(a/b) where b is non-zero.
• Sum/addition rule of square roots: √a + √b ≠ √(a+b) may not be TRUE.

## Simplifying Square Roots

Now, we will provide a step-by-step discussion on how to simplify a square root of a number in its simplest radical form. For example,

Root 8 in radical form: √8 = 2√2.

Square root 12 simplified: √12 = 2√3.

How to simplify root 18: √18 = 2√3.

How to simplify root 20: √20 simplified is 2√5.

How to simplify root 27 in simplest radical form: √27 = 3√3.

Root 50 simplified: √50 = 5√2.

## Square Root of Negative Numbers

Square root of -4: √-4 =2i.

Square root of -9: √-9 = 3i.

Fourth Root: