Simplifying Radicals

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Algebra II › Simplifying Radicals

Questions 1 - 10
1

Simplify.

Explanation

When simplifying radicals, you want to factor the radicand and look for square numbers.

Both the and are not perfect squares, so the answer is just .

2

Factor the radical:

Explanation

The radical can be rewritten with common factors.

Pull out the factor of a known square.

The value of cannot be broken down any further.

The answer is:

3

Simplify the radical.

Cannot be simplified further.

Explanation

Find the factors of 128 to simplify the term.

We can rewrite the expression as the square roots of these factors.

Simplify.

4

Simplify.

Explanation

When simplifying radicals, you want to factor the radicand and look for square numbers.

Both the and are not perfect squares, so the answer is just .

5

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:

6

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.

7

Explanation

When adding or subtracting radicals, the radicand value must be equal. Since and are not the same, we leave the answer as it is. Answer is .

8

Explanation

Adding and subtracting radicals cannot be done without having the same number under the same type of radical. These numbers first need to be simplified so that they have the same number under the radical before adding the coefficients. Look for perfect squares that divide into the number under the radical because those can be simplified.

Now take the square root of the perfect squares. Note that when the numbers come out of the square root they multiply with any coefficients outside that radical.

Since all the terms have the same radical, now their coefficients can be added

9

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:

10

Simplify:

Explanation

We can take the square roots of the numerator and denominator separately. Thus, we get:

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