Simplify Radicals

Front

What is a radical expression?

Back

A radical expression is an expression that includes a root, such as a square root, cube root, etc. For example, √x or ∛(x^2).

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 then take out pairs of factors. For example, √72 = √(36*2) = 6√2.

Front

What is the square root of 72?

Back

The square root of 72 is 6√2.

Front

What does it mean for a radical expression to be in simplest form?

Back

A radical expression is in simplest form when there are no perfect square factors left under the radical sign, and no fractions are present inside the radical.

Front

How do you determine if a radical expression is in simplest form?

Back

Check if there are any perfect square factors under the radical. If there are, simplify the expression by factoring them out.

Front

What is the process for simplifying the expression √(18mn)?

Back

Factor 18 into 9*2, then √(18mn) = √(9*2*mn) = 3√(2mn).

Front

What is the difference between a perfect square and a non-perfect square?

Back

A perfect square is a number that can be expressed as the square of an integer (e.g., 1, 4, 9, 16), while a non-perfect square cannot (e.g., 2, 3, 5).

Front

What is the simplified form of √(50)?

Back

The simplified form of √(50) is 5√2.

Front

How do you simplify the expression √(x^4)?

Back

The simplified form of √(x^4) is x^2, since √(x^4) = x^(4/2) = x^2.

Front

What is the rule for multiplying radicals?

Back

The rule for multiplying radicals states that √a * √b = √(a*b).