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1.8 D) Dividing Surds
1.8 D) Dividing Surds
When we are dividing surds, we follow similar rules to when we are multiplying surds. When we are dividing surds with no numbers in front of them, our answer will be a surd. We obtain the number inside the surd by dividing the number in the first surd by the number in the second surd. We then need to check whether our answer can be simplified. The first two examples in this section will be looking at questions like this.
When we are dividing surds that have numbers on the outside of them, we will get the answer in the form a√b. To obtain a, we divide the number that is on the outside of the first surd by the number that is on the outside of the second surd. To obtain b, we divide the number that is in the first surd by the number that is in the second surd. The last two examples will be looking at questions like this.
Example 1
Complete the calculation below.
Complete the calculation below.
This is a fairly straight forward question because we know that √36 is 6 and √9 is 3. This means that we will be dividing 6 by 3, thus meaning that the answer is 2.
We are now going to use the method that uses surds and we will work the answer out by dividing the number inside the first surd by the number inside the second surd.
This is exactly the same answer as we obtained earlier.
Example 2
Complete the calculation below.
Complete the calculation below.
To find the answer, we divide the number inside the first surd by the number inside the second surd. We therefore divide 95 by 5.
We now need to check that the surd has been given in its simplest form, which it has because there are no square factors in 19.
Example 3
Complete the calculation below.
Complete the calculation below.
Before we start this question, it is a good idea to check whether we are able to simplify any of the surds that are given in the question. There are no square factors that go into 39 or 3 and this means that the surds are already in their simplest form.
We are going to get an answer that is in the form a√b. We obtain the value of a by dividing the number that is on the outside of the first surd by the number that is on the outside of the second surd, which means that we are dividing 4 by 2. Therefore, the value of a is 2.
We now need to obtain b, which is done by dividing the number that is in the first surd by the number that is in the second surd. Therefore, we divide 39 by 3, thus meaning that b is 13.
We are going to get an answer that is in the form a√b. We obtain the value of a by dividing the number that is on the outside of the first surd by the number that is on the outside of the second surd, which means that we are dividing 4 by 2. Therefore, the value of a is 2.
We now need to obtain b, which is done by dividing the number that is in the first surd by the number that is in the second surd. Therefore, we divide 39 by 3, thus meaning that b is 13.
The final step is to check that we have given the answer in its simplest form, which we have because there are no square factors in 13. Therefore, the answer to this question is 2√13.
Example 4
Complete the calculation below.
Complete the calculation below.
The first step is to check whether any of the surds can be simplified. We are unable to simplify the first surd because there are no square factors in 6. But we can simplify the second surd because 18 has a square factor of 9. The process for simplifying the second surd is shown below.
We can now carry out the calculation above with 9√2 rather than 3√18.
The answer will be in the form a√b. We obtain a by dividing the number on the outside of the first surd by the number on the outside of the second surd. Therefore, we divide 27 by 9, which means that a is 3.
We find b by dividing the number inside the first surd by the number inside the second surd. We divide 6 by 2, which means that b is 3.
We find b by dividing the number inside the first surd by the number inside the second surd. We divide 6 by 2, which means that b is 3.
The final step is to check whether our answer is in its simplest form, which we do by looking for any square factors that go into the number that is on the inside of the surd. There are no square factors in 3, which means that our surd is in its simplest form. Therefore, the answer is 3√3.