Simplifying Nth Roots

Front

What is an Nth root?

Back

The Nth root of a number x is a number r such that r^n = x, where n is a positive integer.

Front

How do you simplify the square root of a product?

Back

The square root of a product can be simplified using the property: √(a*b) = √a * √b.

Front

What is the relationship between exponents and roots?

Back

The Nth root of a number can be expressed as an exponent: r = x^(1/n).

Front

How do you simplify the cube root of a quotient?

Back

The cube root of a quotient can be simplified using the property: ∛(a/b) = ∛a / ∛b.

Front

What is the Nth root of a power?

Back

The Nth root of a power can be simplified using the property: ∛(a^m) = a^(m/n).

Front

How do you express a radical in exponential form?

Back

A radical can be expressed in exponential form: √x = x^(1/2), ∛x = x^(1/3), etc.

Front

What is the first step in simplifying radical expressions?

Back

The first step is to factor the expression under the radical into perfect squares (or cubes, etc.) and non-perfect squares.

Front

How do you simplify √(50)?

Back

√(50) = √(25*2) = √25 * √2 = 5√2.

Front

What is the simplified form of ∛(64)?

Back

∛(64) = 4, since 4^3 = 64.

Front

How do you combine like radicals?

Back

Like radicals can be combined by adding or subtracting their coefficients: a√b + c√b = (a+c)√b.