Simplifying Non-Perfect Square Roots with Variables

Front

What is a non-perfect square root?

Back

A non-perfect square root is a square root of a number that cannot be expressed as a whole number. For example, √2 and √3 are non-perfect square roots.

Front

How do you simplify √a²?

Back

√a² simplifies to a, assuming a is non-negative.

Front

What is the first step in simplifying a radical expression?

Back

The first step is to factor the number under the radical into its prime factors.

Front

Simplify √20a²b⁴.

Back

2ab²√5.

Front

What is the square root of 45?

Back

The square root of 45 can be simplified to 3√5.

Front

How do you simplify √(x²y²)?

Back

√(x²y²) simplifies to xy.

Front

What is the simplified form of √(n³)?

Back

√(n³) simplifies to n√n.

Front

Simplify √45x⁴y⁷.

Back

3x²y³√5y.

Front

What is the square root of a product?

Back

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

Front

How do you handle variables when simplifying square roots?

Back

For any variable x, √(x²) simplifies to x, and for odd powers, it simplifies to x raised to the power of (n-1)/2 times √x.