Simplifying Square Roots and Rationalizing the Denominator

Front

What is a perfect square?

Back

A perfect square is a number that can be expressed as the square of an integer. For example, 1, 4, 9, 16, and 25 are perfect squares.

Front

List the first five perfect squares.

Back

1, 4, 9, 16, 25.

Front

What is the square root of 16?

Back

The square root of 16 is 4.

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 of factors. For example, √40 = √(4*10) = √4 * √10 = 2√10.

Front

What is the simplified form of √96?

Back

The simplified form of √96 is 4√6.

Front

What is the process of rationalizing the denominator?

Back

Rationalizing the denominator involves eliminating any square roots or irrational numbers from the denominator of a fraction by multiplying the numerator and denominator by a suitable value.

Front

Simplify the expression: √108.

Back

The simplified form of √108 is 6√3.

Front

Which of the following is NOT a perfect square: 25, 36, 50, 64?

Back

50 is NOT a perfect square.

Front

What is the square root of 25?

Back

The square root of 25 is 5.

Front

Is the statement 4² = √16 true or false?

Back

The statement 4² = √16 is false. 4² = 16, while √16 = 4.