# Square Root Symbol

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Square root symbol is the symbol represented as ‘√’ and is also known as the square root radical sign. Inside this symbol, a number or an expression is written and the number or the expression written inside the square root symbol can be either equal to ‘0’ or can be any positive number, but negative numbers are not allowed inside the radical. If a negative number is inside the radical, then the solution is known as an imaginary solution and they are not real number solutions.

Example 1: What is the value of the square root expression, √4 * √25?

Here each square root number should be simplified further.

√4= √(2 * 2). Now pull out the number which is repeating twice inside the radical.
This gives: 4= 2

Similarly we split ‘25’ to its prime factors, 25 = √(5 * 5) = 5.
So, √4 * √25 = 2 * 5 = 10.

Hence the value of the expression √4 * √25 = 10.

Example 2: What is the value of the square root expression, √18 * √8?

Here each square root number should be simplified further.

√18 = √(2 * 3 * 3). Now pull out the number which is repeating twice inside the radical.

This gives: 18 = 3 * √2 = 3√2.

Similarly, 8 = √(2 * 2 * 2) = 2 * √2 = 2√2.

So, √18 * √8 = 3√2* 2√2 = (3 * 2) √(2 * 2) = 6 * 2 = 12.

Hence the value of the expression √18 * √8 = 12.