Simplifying Square Roots (with variables)

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 √(a^2)?

Back

√(a^2) simplifies to |a|, which is the absolute value of a.

Front

What is the square root of a product?

Back

The square root of a product is the product of the square roots. For example, √(ab) = √a * √b.

Front

How do you simplify √(x^2y)?

Back

√(x^2y) simplifies to |x|√y.

Front

What is the square root of a quotient?

Back

The square root of a quotient is the quotient of the square roots. For example, √(a/b) = √a / √b.

Front

How do you simplify √(x^4)?

Back

√(x^4) simplifies to x^2.

Front

What is the principle of simplifying square roots with variables?

Back

The principle involves factoring out perfect squares from under the square root and simplifying accordingly.

Front

How do you handle square roots of negative numbers?

Back

Square roots of negative numbers involve imaginary numbers. For example, √(-1) = i.

Front

What is a perfect square?

Back

A perfect square is an integer that is the square of another integer. For example, 1, 4, 9, 16 are perfect squares.

Front

How do you simplify √(16x^2)?

Back

√(16x^2) simplifies to 4|x|.