Operations with Radicals

Front

What is a radical in mathematics?

Back

A radical is an expression that includes a root, such as a square root (√) or cube root (∛). It represents the inverse operation of exponentiation.

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 of two radicals?

Back

The product of two radicals can be simplified by multiplying the numbers under the radicals together, then simplifying the resulting radical if possible.

Front

What is the sum of two radicals?

Back

The sum of two radicals can only be simplified if the radicals have the same index and radicand (the number under the radical). Otherwise, they remain separate.

Front

What is the difference between rational and irrational numbers?

Back

Rational numbers can be expressed as a fraction of two integers, while irrational numbers cannot be expressed as a simple fraction and have non-repeating, non-terminating decimal expansions.

Front

How do you rationalize the denominator?

Back

To rationalize the denominator, multiply the numerator and denominator by a suitable radical that will eliminate the radical in the denominator.

Front

What is the square root of 16?

Back

The square root of 16 is 4, since 4 x 4 = 16.

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