What Is the Square Root of 135?

The positive square root of 135 simplifies to 3 times the square root of 15, or 3 * sqrt(15). When using a calculator, the decimal value representing the square root of 135 is approximately 11.61895003862225. The negative of this value is also a square root of 135.

Each positive number has a positive and negative square root. These two square roots have the same absolute value. When the negative root is multiplied by itself, the product becomes positive. In the case of the square roots of 135, both (3 * sqrt(15))^2 and (-3 * sqrt(15))^2 equal 135. Note that the term "sqrt" represents taking the square root of the number.

The reason that the positive square root of 135 simplifies to 3 * sqrt(15) is because sqrt(135) = sqrt(9 * 15) = sqrt(9) * sqrt(15) = 3 * sqrt(15). The square root of 15 has no factor greater than 1 that is a square of another integer, so this term is not simplified any further.