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1.8 B) Multiplying Surds – Part 1
1.8 B) Multiplying Surds – Part 1
Whenever we are multiplying two surds that are the same as each other, the answer will be the number that is inside the surd. For example,
Sometimes this may be written as (√6)2, which is the base, √6, multiplied by itself.
Another way to look at it is to use indices. Square rooting has the power ½, therefore we can write √6 x √6 as:
Whenever we are multiplying powers with the same base, we add the powers.
Anything to the power of 1 is itself, which means that the answer is 6.
The Rule
The rule in algebraic terms is:
The Rule
The rule in algebraic terms is:
Multiplying Surds – Not the Same
The rule for multiplying surds that do not have the same number inside the surd is given below.
The rule for multiplying surds that do not have the same number inside the surd is given below.
Example 1
Complete the calculation below.
Complete the calculation below.
We find the answer to this question by multiplying the numbers that are inside each of the surds.
Usually the answer will not be able to be simplified but it is always worth double checking. There are no square factors in 30, which means that the surd is already given in its simplest form.
Example 2
The rule above works for the multiplying of surds that are the same.
For example; complete the calculation below.
The rule above works for the multiplying of surds that are the same.
For example; complete the calculation below.
I am going to complete this calculation by using both of the rules above. The first rule is that when you are multiplying a surd by itself, you obtain the value that was inside the surd; √a x √a = a. This means that the answer will be 3.
The other rule is that you multiply surds by multiplying the numbers that are inside the surds; √a x √b = √ab.
You can see that both of these rules give you the same answer.
Example 3
Complete the calculation below.
Complete the calculation below.
The values inside the surds are not the same, which means that we find the answer to this question by multiplying the numbers that are inside each of the surds.
We now need to check whether there are any square factors in the number that is inside the surd (20). 4 is a square factor of 20 and this means that our surd can be simplified.
There are no more square factors in 5, which means that the surd is now in its simplest form; the answer is 2√5.
Example 4 -Multiplying 3 Surds
If we were multiplying 3 surds together, we would multiply the 3 numbers that are inside each of the 3 surds. For example, complete the calculation below.
If we were multiplying 3 surds together, we would multiply the 3 numbers that are inside each of the 3 surds. For example, complete the calculation below.
We obtain the answer by multiplying all of the numbers that are on the inside of the surds.
There are no square factors in 42, which means that this surd is in its simplest form; the answer to this question is √42.