Multiplying and Dividing Radicals

What is the product of two radicals?

• To multiply two radicals, multiply the numbers outside the radicals and the numbers inside the radicals separately. For example, @@ ext{If } a = ext{√}m ext{ and } b = ext{√}n, ext{ then } a imes b = ext{√}(m imes n)@@.

• The product of two radicals is always a radical of the sum of the two numbers.

• The product of two radicals is equal to the difference of the two numbers inside the radicals.

• To multiply two radicals, simply add the numbers inside the radicals.

How do you rationalize the denominator of @@\frac{1}{\text{√}a}@@?

• Multiply the numerator and denominator by @@\text{√}a@@ to get @@\frac{\text{√}a}{a}@@.

• Add @@\text{√}a@@ to the numerator and denominator.

• Multiply the numerator by @@\text{√}a@@ and leave the denominator unchanged.

• Subtract @@\text{√}a@@ from both the numerator and denominator.

• 6

• 3

• 12

• 6\text{√}1 = 6

Define a radical.

• An expression that includes a root, such as a square root (√) or cube root (∛).

• A type of polynomial that has no variables.

• A mathematical operation that combines two numbers.

• A geometric figure with straight lines.

What is the product of @@ ext{√}a ext{ and } ext{√}b?@@

• @@ ext{√}(a imes b)@@

• @@ ext{√}(a + b)@@

• @@a + b@@

• @@a imes b@@

What is the simplified form of @@ ext{√}50@@?

• @@5 ext{√}2@@

• @@10@@

• @@ ext{√}25@@

• @@ ext{√}50@@

Simplify: @@\frac{\text{√}32}{\text{√}2}@@

• 2

• 4

• 8

• 16

Simplify: @@\frac{4\text{√}50}{2\text{√}2}@@

• 5

• 8

• 10

• 12