**Surds**

Another way that these questions can be made more complex is to have surds involved. The power for a square root is ½ or 0.5.

So, if we had the equation below:

*c*would be ½ or 0.5.

**Example 1**

We have the equation below:

*d*.

This question is essentially saying “6 to the power of what gives us 36√6”. I am going to answer this question by working with the right side of the equation. Currently, the right side of the equation is saying 36 lots of √6. This means that we can add in a multiplication sign between the two terms to get:

The adding in of the multiplication sign on the right side of the equation makes it easier to work with and you will see why in a few steps time. We now need to write each of the terms (36 and √6) in the form of the base number on the left side of the equation to the power of *something*. The base number on the left side of the equation is 6. Therefore, we are going to write 36 and √6 as 6* ^{something}*; 36 when written as 6

*is 6*

^{something}^{2}, and √6 when written as 6

*is 6*

^{something}^{0.5}(or 6

^{½}). This results in the right side of the equation becoming:

*d*is 2.5.

**Example 2**

We have the equation:

*e*.

Like the previous example, I am just going to work with the right side of the equation. The right side of the equation is saying 27 lots of √3, and this means that we can add in a multiplication sign between the two terms. This results in the right side of the equation becoming:

We now need to write each of the terms (27 and √3) in the form of the base number on the left side of the equation to the power of *something*. The base number on the left side of the equation is 3. Therefore, we are going to write 27 and √3 as 3* ^{something}*; 27 when written as 3

*is 3*

^{something}^{3}, and √3 when written as 3

*is 3*

^{something}^{0.5}(or 3

^{½}). This results in the right side of the equation becoming:

*e*is 3.5.