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 is a radical expression.

Front

How do you simplify a radical expression?

Back

To simplify a radical expression, factor the number under the radical into its prime factors, and then simplify by taking out pairs of factors for square roots.

Front

What is the product property of square roots?

Back

The product property states that the square root of a product is equal to the product of the square roots: √(a*b) = √a * √b.

Front

What is the quotient property of square roots?

Back

The quotient property states that the square root of a quotient is equal to the quotient of the square roots: √(a/b) = √a / √b.

Front

How do you multiply two radical expressions?

Back

To multiply two radical expressions, use the product property of square roots: √a * √b = √(a*b) and then simplify if possible.

Front

What is the simplified form of √32?

Back

The simplified form of √32 is 4√2.

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

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The simplified form of √(a^4) is a^2.

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How do you simplify √(121a^4b^6)?

Back

To simplify √(121a^4b^6), factor it as √(121) * √(a^4) * √(b^6) = 11 * a^2 * b^3 = 11a^2b^3.

Front

What does it mean to rationalize the denominator?

Back

Rationalizing the denominator means to eliminate any radicals in the denominator of a fraction by multiplying the numerator and denominator by a suitable radical.

Front

What is the difference between a perfect square and a non-perfect square?

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A perfect square is a number that can be expressed as the square of an integer (e.g., 1, 4, 9, 16), while a non-perfect square cannot (e.g., 2, 3, 5).