Chapters

What are Radicals?
Multiplying Radicals
Example 1
Example 2
Example 3
Example 4
Example 5
Example 6
Example 7
Example 8
Example 9
Example 10
Example 11
Example 12
Example 13
Example 14
Example 15

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What are Radicals?

The radical is also known as a root and it is the inverse operation of applying exponent. It means that we can remove power by taking a radicals and we can remove a radical by taking power. For example, if we take a square of 4, we will get 16 and when we will take a square root of 16, we will get 4. Similarly, if we take the cube of 2, we will get 8 and if we will get a cube root of 8, we will get 2. Mathematically, we can write these examples like this:

$\text{[math]}$ , $\text{[math]}$

$\text{[math]}$ is the radical symbol and the number inside this symbol is known as the radicand. We can read the expression $\text{[math]}$ as square root 16, root 16, or radical 16.

In the next section, we will discuss how to multiply radical expressions.

Multiplying Radicals

We can apply the operations of addition, subtraction, multiplication, and division on radicals just like numbers. Radicals are multiplied together by multiplying their radicands (the terms inside the radical symbol). The product of radicands is kept under the same radical sign. Now, let us see how to multiply radicals practically through a couple of examples.

Example 1

Multiply $\text{[math]}$

Solution

We will simply multiply the terms inside the radical symbol together. The radicands in this example are 6 and 10. The product of 6 and10 is equal to 60. Hence, the final answer will be:

= $\text{[math]}$

$\text{[math]}$ can be simplified further because 60 is equal to 2 x 3 x 5 x 2.

= $\text{[math]}$

Example 2

Multiply $\text{[math]}$

Solution

We will simply multiply the terms inside the radical symbol together. The radicands in this example are 8 and 6. The product of 8 and 6 is equal to 48. Hence, the final answer will be:

= $\text{[math]}$

$\text{[math]}$ can be simplified further because 48 is equal to 2 x 2 x 2 x 2 x 3.

= $\text{[math]}$

Example 3

Multiply $\text{[math]}$

Solution

We will simply multiply the terms inside the radical symbol together. The radicands in this example are 9 and 5. The product of 9 and 5 is equal to 45. Hence, the final answer will be:

= $\text{[math]}$

$\text{[math]}$ can be simplified further because 45 is equal to 3 x 3 x 5.

= $\text{[math]}$

Example 4

Multiply $\text{[math]}$

Solution

We will simply multiply the terms inside the radical symbol together. The radicands in this example are 27 and 2. The product of 27 and 2 is equal to 54. Hence, the final answer will be:

= $\text{[math]}$

$\text{[math]}$ can be simplified further because 54 is equal to 3 x 3 x 3 x 2.

= $\text{[math]}$

Example 5

Multiply $\text{[math]}$

Solution

We will simply multiply the terms inside the radical symbol together. The radicands in this example are 4y and $\text{[math]}$ . The product of 4y and $\text{[math]}$ is equal to $\text{[math]}$ . Hence, the final answer will be:

= $\text{[math]}$

The answer can be simplified further because $\text{[math]}$ is equal to $\text{[math]}$ .

= $\text{[math]}$

Example 6

Multiply $\text{[math]}$

Solution

We will simply multiply the terms inside the radical symbol together. The radicands in this example are 8x and $\text{[math]}$ . The product of 8x and $\text{[math]}$ is equal to $\text{[math]}$ . Hence, the final answer will be:

= $\text{[math]}$

The answer can be simplified further because $\text{[math]}$ is equal to $\text{[math]}$ .

= $\text{[math]}$

Example 7

Multiply $\text{[math]}$

Solution

We will simply multiply the terms inside the radical symbol together. The radicands in this example are $\text{[math]}$ and $\text{[math]}$ . The product of $\text{[math]}$ and $\text{[math]}$ is equal to $\text{[math]}$ . Hence, the final answer will be:

= $\text{[math]}$

The answer can be simplified further because $\text{[math]}$ is equal to $\text{[math]}$ .

= $\text{[math]}$

Example 8

Multiply $\text{[math]}$

Solution

$\text{[math]}$ is equal to 2. Hence, 2 multiplied by $\text{[math]}$ is equal to 4. It can be written as:

= $\text{[math]}$

Example 9

Multiply $\text{[math]}$

Solution

$\text{[math]}$ is equal to 4. Hence, 5 multiplied by $\text{[math]}$ is equal to 20. It can be written as:

= $\text{[math]}$

Example 10

Multiply $\text{[math]}$

Solution

= $\text{[math]}$

The answer can be simplified further because $\text{[math]}$ is equal to $\text{[math]}$ .

= $\text{[math]}$

Example 11

Multiply $\text{[math]}$

Solution

We will simply multiply the terms inside the radical symbol together. The radicands in this example are 125 and 2. The product of 125 and 2 is equal to 250. Hence, the final answer will be:

= $\text{[math]}$

$\text{[math]}$ can be simplified further because 250 is equal to 5 x 5 x 5 x 2.

= $\text{[math]}$

Example 12

Multiply $\text{[math]}$

Solution

We will simply multiply the terms inside the radical symbol together. The radicands in this example are 9 and 1000. The product of 9 and 1000 is equal to 9000. Hence, the final answer will be:

= $\text{[math]}$

$\text{[math]}$ can be simplified further because 9000 is equal to 2 x 5 x 2 x 5 x 2 x 5 x 3 x 3.

= $\text{[math]}$

Example 13

Multiply $\text{[math]}$

Solution

We will simply multiply the terms inside the radical symbol together. The radicands in this example are 8 and 9. The product of 8 and 9 is equal to 72. Hence, the final answer will be:

= $\text{[math]}$

$\text{[math]}$ can be simplified further because 72 is equal to 2 x 2 x 2 x 3 x 3.

= $\text{[math]}$

Example 14

Multiply $\text{[math]}$

Solution

We will simply multiply the terms inside the radical symbol together. The radicands in this example are 7 and 8. The product of 7 and 8 is equal to 56. Hence, the final answer will be:

= $\text{[math]}$

$\text{[math]}$ can be simplified further because 56 is equal to 7 x 2 x 2 x 2.

= $\text{[math]}$

Example 15

Multiply $\text{[math]}$

Solution

We will simply multiply the terms inside the radical symbol together. The radicands in this example are 8 and 10. The product of 8 and 10 is equal to 80. Hence, the final answer will be:

= $\text{[math]}$

$\text{[math]}$ can be simplified further because 80 is equal to 2 x 2 x 2 x 5 x 2.

= $\text{[math]}$

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Multiplying Radicals

What are Radicals?

Multiplying Radicals

Example 1

Solution

Example 2

Solution

Example 3

Solution

Example 4

Solution

Example 5

Solution

Example 6

Solution

Example 7

Solution

Example 8

Solution

Example 9

Solution

Example 10

Solution

Example 11

Solution

Example 12

Solution

Example 13

Solution

Example 14

Solution

Example 15

Solution

Theory

Real Numbers

Power of Radicals

Radicals

Rationalizing Denominators with Radicals

Absolute Value

Root of Radicals

Dividing Radicals

Half-line

Intervals

Irrational Numbers

Operations with Real Numbers

Adding Radicals

Powers

Multiplying Radicals

Formulas

Power Formulas

Radical Formulas

Exercises

Radicals Worksheet

Real Numbers Worksheet

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