Operations with Radicals Review (Adv Alg)

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{ } oot{3}{x}@@ is a radical expression.

Front

How do you simplify a square root?

Back

To simplify a square root, factor the number under the root into its prime factors and look for pairs. For example, @@ ext{ } oot{2}{20} = oot{2}{4 imes 5} = 2 oot{2}{5}@@.

Front

What is the product property of radicals?

Back

The product property states that @@ oot{n}{a} imes oot{n}{b} = oot{n}{a imes b}@@.

Front

What is the quotient property of radicals?

Back

The quotient property states that @@ oot{n}{rac{a}{b}} = rac{ oot{n}{a}}{ oot{n}{b}}@@, provided that b is not zero.

Front

How do you add or subtract radical expressions?

Back

You can only add or subtract radical expressions that have the same index and radicand. For example, @@ oot{2}{3} + oot{2}{3} = 2 oot{2}{3}@@.

Front

What is the first step in simplifying @@-2 oot[]{5x}+3 oot[]{20x}@@?

Back

Front

What is the simplified form of @@3 oot[]{6x^2}-2 oot[]{20x^3}+2x oot[]{45x}@@?

Back

The simplified form is @@3x oot[]{6}+2x oot[]{5x}@@.

Front

How do you multiply radical expressions?

Back

To multiply radical expressions, multiply the coefficients and the radicands separately. For example, @@3 oot[3]{12} imes 7 oot[3]{18} = 21 oot[3]{216} = 126@@.

Front

What is the simplified form of @@ oot[]{50}@@?

Back

Front

What is the difference between a square root and a cube root?

Back

A square root (index 2) finds a number that, when multiplied by itself, gives the original number. A cube root (index 3) finds a number that, when multiplied by itself three times, gives the original number.