Simplifying Square Roots with and without variables

Front

What is a square root?

Back

A square root of a number x is a value y such that y² = x. For example, the square root of 25 is 5, since 5² = 25.

Front

How do you simplify a square root?

Back

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

Front

What is the square root of 100?

Back

The square root of 100 is 10, since 10² = 100.

Front

How do you simplify √(a²b)?

Back

√(a²b) = a√b, where a is a positive number.

Front

What is the square root of a variable squared?

Back

The square root of a variable squared, such as √(x²), is |x|, which represents the absolute value of x.

Front

How do you handle square roots with variables?

Back

When simplifying square roots with variables, apply the same rules as with numbers, taking out pairs of variables as you would pairs of numbers.

Front

What is the simplified form of √(50)?

Back

The simplified form of √(50) is 5√2, since 50 = 25 * 2 and √(25) = 5.

Front

What is the product property of square roots?

Back

The product property states that √(a * b) = √a * √b for any non-negative numbers a and b.

Front

What is the quotient property of square roots?

Back

The quotient property states that √(a / b) = √a / √b for any non-negative numbers a and b, where b ≠ 0.

Front

How do you simplify √(x²y³)?

Back

√(x²y³) = x√(y²y) = xy√y.