A11A - A11B Simplify Radicals/Rational Exponents

Front

What is a radical?

Back

A radical is an expression that includes a root, such as a square root (√) or cube root (∛).

Front

What does it mean to simplify a radical?

Back

To simplify a radical means to express it in its simplest form, removing any perfect square factors from under the radical sign.

Front

What is a rational exponent?

Back

A rational exponent is an exponent that is a fraction, indicating both a power and a root. For example, x^(1/2) is the square root of x.

Front

How do you convert a radical expression to a rational exponent?

Back

To convert a radical expression to a rational exponent, use the formula: √a = a^(1/2) and ∛a = a^(1/3).

Front

What is the product property of radicals?

Back

The product property states that √a * √b = √(a*b).

Front

What is the quotient property of radicals?

Back

The quotient property states that √(a/b) = √a / √b.

Front

How do you simplify √(50)?

Back

√(50) can be simplified to 5√2, since 50 = 25 * 2 and √25 = 5.

Front

What is the relationship between rational exponents and roots?

Back

Rational exponents represent roots; for example, x^(1/n) represents the n-th root of x.

Front

How do you simplify x^(3/2)?

Back

x^(3/2) can be expressed as √(x^3) or (√x)^3.

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.