Simplifying Radicals - nth Roots

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 ∛y.

Front

What does it mean to simplify a radical expression?

Back

To simplify a radical expression means to rewrite it in a simpler form, often by removing perfect squares, cubes, etc., from under the radical sign.

Front

What is the nth root of a number?

Back

The nth root of a number 'a' is a number 'b' such that b^n = a. For example, the cube root of 8 is 2 because 2^3 = 8.

Front

How do you simplify √(a*b)?

Back

√(a*b) = √a * √b, provided that a and b are non-negative.

Front

What is the square root of 16?

Back

The square root of 16 is 4, since 4^2 = 16.

Front

How do you simplify √(x^2)?

Back

√(x^2) = |x|, which means the absolute value of x.

Front

What is the cube root of 27?

Back

The cube root of 27 is 3, since 3^3 = 27.

Front

How do you simplify √(a^2 * b)?

Back

√(a^2 * b) = a√b, where a is non-negative.

Front

What is the relationship between exponents and roots?

Back

The nth root of a number can be expressed as an exponent: a^(1/n) is the nth root of a.

Front

How do you simplify a radical expression with a coefficient?

Back

For example, to simplify 3√(12), first simplify √(12) to 2√(3), then multiply: 3 * 2√(3) = 6√(3).