Simplifying Square Roots

Front

What is a square root?

Back

A square root of a number x is a number y such that y² = x. For example, the square root of 9 is 3 because 3² = 9.

Front

How do you simplify a square root?

Back

To simplify a square root, factor the number under the square root into its prime factors and look for pairs of factors. Each pair can be taken out of the square root as a single factor.

Front

What is the square root of 12 simplified?

Back

The square root of 12 can be simplified to 2√3, since 12 = 4 * 3 and √4 = 2.

Front

What is the square root of 10√2?

Back

The expression 10√2 is already in its simplest form. It represents 10 times the square root of 2.

Front

What is the square root of 2√3?

Back

The expression 2√3 is already in its simplest form. It represents 2 times the square root of 3.

Front

What is the square root of 2√5?

Back

The expression 2√5 is already in its simplest form. It represents 2 times the square root of 5.

Front

What is the product of two square roots?

Back

The product of two square roots can be simplified using the property √a * √b = √(a*b). For example, √2 * √3 = √6.

Front

What is the sum of two square roots?

Back

The sum of two square roots cannot be simplified in the same way as products. For example, √2 + √3 remains as is.

Front

How do you rationalize the denominator?

Back

To rationalize the denominator, multiply the numerator and denominator by a suitable value that will eliminate the square root in the denominator.

Front

What is the square root of a fraction?

Back

The square root of a fraction a/b is equal to the square root of the numerator divided by the square root of the denominator: √(a/b) = √a / √b.