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TopTo learn how to subtract Radicals with different radicands, we must know that only radicals with the same base are added, so we say that when we come across the situations in which radicals with the different bases are given, we should not assume that the radicals with the different bases cannot be added or subtracted. We will proceed in the following way:
To find the difference between the pair of radicals in case the radicands are different, we will first find the factors of the given radical and then try to express both the radicals with the same base. We will form the Sets of the factors such that some of the whole Numbers of the radicals comes out and the figures look like the Combination of whole numbers and the roots.
Suppose we have to find the difference of 4 * √ (5) and √ (45)
= 4 * √ (5) - √ (45),
Here we observe that two root values are quite different. So in such a situation we will first find the factors of 45 and we get:
√ (45) = √ (5 * 9),
= √ (5 * 3 * 3),
Now we will find that √ (3 * 3) = 3, so we say that √ (45) can be written as 3 * √ (5).
Thus we say that we can write the given question in the following form:
= 4 * √ (5) - 3 * √ (5),
= Now we observe that the radical in both the terms are same so we can easily perform the difference between the two numbers and we get
= (4 – 3) * √( 5 )
= 1 √ ( 5).