Radicals & Simplifying Radical Expression

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, @@ ext{radical expression} = ext{ } oot{n}{x}@@.

Front

What does it mean to simplify a radical expression?

Back

To simplify a radical expression means to rewrite it in a simpler form, usually by removing any perfect square factors from the radicand.

Front

Simplify @@rac{8}{ ext{ } oot{6}{}}@@.

Back

@@rac{4 ext{ } oot{6}{}}{3}@@.

Front

What is the process of rationalizing the denominator?

Back

Rationalizing the denominator involves eliminating any radicals in the denominator of a fraction by multiplying the numerator and denominator by a suitable radical.

Front

Simplify @@ ext{ } oot{88}@@.

Back

@@2 ext{ } oot{22}@@.

Front

What is a radicand?

Back

Front

Explain why @@rac{7 ext{ } oot{3}{}}{ ext{ } oot{10}{}}@@ is not in simplified form.

Back

The expression is not in simplified form because it contains a radical in the denominator.

Front

What is the square root of a number?

Back

Front

Simplify @@rac{10}{ ext{ } oot{12}{}}@@.

Back

@@rac{5 ext{ } oot{3}{}}{3}@@.

Front

What does it mean for a radical to be in simplest form?

Back

A radical is in simplest form when the radicand has no perfect square factors other than 1, and there are no radicals in the denominator.