Radicals

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Algebra II › Radicals

Questions 1 - 10
1

Evaluate:

Explanation

Raise both sides by the power of three.

Subtract three from both sides.

Divide both sides by negative nine.

The answer is:

2

Simplify:

Explanation

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

3

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:

4

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 .

5

Simplify:

Explanation

This expression can either be split into common factors of perfect squares, or this can be multiplied as one term.

For the simplest method, we will multiply the two numbers in radical form to combine as one radical.

The square root of a number is another number multiplied by itself to achieve the number in the square root.

The answer is:

6

Solve.

Explanation

When adding and subtracting radicals, make the sure radicand or inside the square root are the same.

If they are the same, just add the numbers in front of the radical.

Since they are not the same, the answer is just the problem stated.

7

The answer is not present

Explanation

We can only combine radicals that are similar or that have the same radicand (number under the square root).

Combine like radicals:

We cannot add further.

Note that when adding radicals there is a 1 understood to be in front of the radical similar to how a whole number is understood to be "over 1".

8

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.

9

Simplify.

Explanation

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

10

Solve for .

Explanation

To get rid of the radical, we square both sides.

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