Simplifying Radicals

Front

What is a radical in mathematics?

Back

A radical is a symbol used to represent the root of a number, most commonly the square root. For example, √x represents the square root of x.

Front

How do you simplify a radical expression?

Back

To simplify a radical expression, factor the number under the radical into its prime factors, then pair the factors to take them out of the radical.

Front

What is the square root of 64?

Back

The square root of 64 is 8.

Front

What is the simplified form of √32?

Back

The simplified form of √32 is 4√2.

Front

How do you simplify √48?

Back

To simplify √48, factor it as √(16*3) = √16 * √3 = 4√3.

Front

What is the simplified form of √(50x^4)?

Back

The simplified form of √(50x^4) is 5x^2√2.

Front

What is the process to simplify √(64x^4z^6)?

Back

To simplify √(64x^4z^6), factor it as √(64) * √(x^4) * √(z^6) = 8x^2z^3.

Front

What does it mean to rationalize the denominator?

Back

Rationalizing the denominator means to eliminate any radicals from the denominator of a fraction.

Front

What is the product property of square roots?

Back

The product property states that √(a*b) = √a * √b for any non-negative numbers a and b.

Front

What is the quotient property of square roots?

Back

The quotient property states that √(a/b) = √a / √b for any non-negative numbers a and b, where b ≠ 0.