Multiplying and Dividing Radicals

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Algebra II › Multiplying and Dividing Radicals

Questions 1 - 10
1

Simplify.

Explanation

When multiplying radicals, you can combine them and multiply the numbers inside the radical.

2

Multiply the radicals:

Explanation

In order to multiply these radicals, we are allowed to multiply all three integers to one radical, but the final term will need to be simplified.

Instead, we can pull out common factors in order to simplify the terms.

Rewrite the expression.

A radical multiplied by itself will give just the integer.

The answer is:

3

Simplify:

Explanation

When multiplying radicals, simply multiply the numbers inside the radical with each other. Therefore:

We cannot further simplify because both of the numbers multiplied with each other were prime numbers.

4

Simplify.

Explanation

When multiplying radicals, you can combine them and multiply the numbers inside the radical. NUmbers outside the radical are also multiplied.

We can simplify this.

5

Multiply:

Explanation

It is possible to multiply all the integers together to form one radical, but doing so will give a square root of a value that will need to be factored.

Instead, rewrite each square root by their factors.

A radical multiplied by itself will become the integer. Simplify the expression.

The answer is:

6

Simplify:

Explanation

When multiplying radicals, simply multiply the numbers inside the radical with each other. Therefore:

We can simplify this by factoring and finding perfect perfect squares.

7

Explanation

Combine radicals:

Simplify the radical leftover:

8

Simplify.

Explanation

When multiplying radicals, you can combine them and multiply the numbers inside the radical.

We can simplify this. Lets find a perfect square.

9

Simplify .

It cannot be simplified any further.

Explanation

The Quotient Raised to a Power rule states that .

Remember that a square root is the equivalent of raising a term to the 1/2 power.

In this case:

10

Simplify:

Explanation

When we multiply expressions containing both radicals and whole numbers, we simply multiply the numbers inside the radical with each other and those outside the radical with each other.

.

We can simplify this by factoring and finding perfect perfect squares.

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