Simplifying Square Roots

Front

What is a square root?

Back

A square root of a number is a value that, when multiplied by itself, gives the original number. For example, the square root of 9 is 3, because 3 x 3 = 9.

Front

How do you simplify the square root of a perfect square?

Back

To simplify the square root of a perfect square, find the number that, when squared, equals the original number. For example, √16 = 4.

Front

What is the square root of 25?

Back

The square root of 25 is 5, because 5 x 5 = 25.

Front

How do you simplify the square root of a non-perfect square?

Back

To simplify the square root of a non-perfect square, factor the number into its prime factors and look for pairs. For example, √18 = √(9 x 2) = √9 x √2 = 3√2.

Front

What is the square root of 50 simplified?

Back

The square root of 50 can be simplified to 5√2, because √50 = √(25 x 2) = √25 x √2 = 5√2.

Front

What does it mean to rationalize the denominator?

Back

Rationalizing the denominator means to eliminate any square roots from the denominator of a fraction. For example, to rationalize 1/√2, multiply the numerator and denominator by √2 to get √2/2.

Front

What is the square root of 64?

Back

The square root of 64 is 8, because 8 x 8 = 64.

Front

How do you express the square root of a fraction?

Back

The square root of a fraction can be expressed as the square root of the numerator divided by the square root of the denominator. For example, √(4/9) = √4 / √9 = 2/3.

Front

What is the square root of 81?

Back

The square root of 81 is 9, because 9 x 9 = 81.

Front

How do you simplify √(a^2)?

Back

The square root of a squared variable is the absolute value of that variable. For example, √(x^2) = |x|.