Simplifying Radical Expressions

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{2}{x}@@ is a radical expression.

Front

How do you simplify @@ ext{ } oot{2}{a^2}@@?

Back

@@ ext{ } oot{2}{a^2} = a@@, since the square root of a squared number is the number itself.

Front

What is the process of simplifying radical expressions?

Back

To simplify radical expressions, factor the number under the radical into its prime factors and look for pairs of factors. Each pair can be taken out of the radical.

Front

Simplify @@5 oot{2}{200} - 5 oot{2}{8}@@.

Back

@@40 oot{2}{2}@@.

Front

Back

C) @@4 oot{5} - 4 oot{7}@@ cannot be added or subtracted because the radicals are different.

Front

Simplify @@3 oot{2}{12} - 2 oot{2}{18} + 4 oot{2}{48} - 6 oot{2}{72}@@.

Back

@@22 oot{3} - 42 oot{2}@@.

Front

Add: @@4 oot{7} - 10 oot{7} + 7 oot{7}@@.

Back

@@ oot{7}@@.

Front

Simplify @@-2 oot{2} - 3 oot{8} - oot{5}@@.

Back

@@-8 oot{2} - oot{5}@@.

Front

What is the square root of a product?

Back

The square root of a product is equal to the product of the square roots. For example, @@ oot{2}{ab} = oot{2}{a} imes oot{2}{b}@@.

Front

What is the square root of a quotient?

Back

The square root of a quotient is equal to the quotient of the square roots. For example, @@ oot{2}{rac{a}{b}} = rac{ oot{2}{a}}{ oot{2}{b}}@@.