Question

What is the square root of 640?
(a) 80
(b) $8\sqrt{10}$
(c) $6\sqrt{10}$
(d) None of these

Answer 1

Hint: In this problem, we are trying to find the square root of the given integer 640. First, we will try factoring and find the matching terms. Once we find the terms which are repeating, we take them out of the root term. Thus, after simplification, we get the solution we need.

Complete step by step solution:
According to the question, we are trying to find the square root of 640.
To find the square root of a given fraction we need to find square roots of the number after factoring.
We have our number as 640.
And we also see, $640=2\times 2\times 2\times 2\times 2\times 2\times 2\times 5$
Thus, the square root of 122 gives us, $\sqrt{640}=\sqrt{2\times 2\times 2\times 2\times 2\times 2\times 2\times 5}$ .
Now, we can see that both of the terms 2 and 5, 2 is repeating 7 times and 5 is not repetitive, hence we can not take 5 out of the root sign and also check how many pairs of 2’s we are getting.
Now, by checking out, we can see that we have 3 pairs of 2’s and one 2 as a single.
Then, the square root of 640 provides us, $\sqrt{640}=2\times 2\times 2\sqrt{2\times 5}=8\sqrt{10}$ .
Writing this into a proper form, we are getting $8\sqrt{10}$.
Thus, we have our solution, $8\sqrt{10}$.
We have our solution as, (b) $8\sqrt{10}$.

Note: There are lots of techniques to find the square root of a number. Some of them are listed below -1. Prime Factorization Method and 2. Division Method. For the Prime Factorization Method, In this Method, we had to break down a number into its factors until all the numbers left are prime. We take the least factor. If we take the wrong factor then our answer would be incorrect.