Alg 2 - Lesson 6.1-6.3 Review

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.

Front

How do you simplify a radical expression?

Back

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

Front

What is the value of -∜625?

Back

-5

Front

What does it mean to rationalize a denominator?

Back

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

Front

How do you rationalize the denominator of \( \frac{4}{1 + \sqrt{3}} \)?

Back

Multiply the numerator and denominator by the conjugate of the denominator, which is \( 1 - \sqrt{3} \).

Front

What is the result of rationalizing \( \frac{4}{1 + \sqrt{3}} \)?

Back

The result is \( -2 + 2\sqrt{3} \).

Front

How do you rationalize the denominator of \( \frac{5}{\sqrt{7} + 2} \)?

Back

Multiply the numerator and denominator by the conjugate of the denominator, which is \( \sqrt{7} - 2 \).

Front

What is the simplified form of \( \frac{5}{\sqrt{7} + 2} \) after rationalizing?

Back

The simplified form is \( \frac{5\sqrt{7} - 10}{3} \).

Front

What is the principle behind simplifying radical expressions?

Back

The principle is to express the radical in its simplest form by removing perfect squares or higher powers from under the radical.

Front

What is a conjugate in the context of rationalizing denominators?

Back

The conjugate of a binomial expression \( a + b \) is \( a - b \).