Question

The product of two numbers is $37$. What is the square root of their difference?

Answer 1

Hint:
Assume the numbers to be ‘a’ and ‘b’. Here we can see that $37$ is a prime number. Prime numbers are numbers that are only divisible by themselves and $1$. Then find the difference of the obtained numbers and at last find the square root of the difference obtained.

Complete step by step solution:
Given, the product of two numbers is$37$.We have to find the square root of their differences.
 If ‘a’ and b are the two numbers whose product is $37$ then we are going to find $a - b$ first, then if $a - b = c$ (let) then we are going to find its square root. i.e.$\sqrt c $
We now that $37$is a prime number which means it has only two factors $37$ and $1$ so we know the value of ‘a’ and ‘b’ Now we are going to find$a - b$. On Subtracting b from a, we get-
$ \Rightarrow 37 - 1 = 36$
Now, we have to find the square-root of $36$. We know that$36$ is a perfect square.
We can find its square root by finding its factors by dividing it by the smallest prime number which is $2$
$ \Rightarrow \dfrac{{36}}{2} = 18$
Then again divide the obtained number by the smallest prime number (from which the number is divisible)
$ \Rightarrow \dfrac{{18}}{2} = 9$
Then again divide the obtained number by the smallest prime number (from which the number is divisible)
$ \Rightarrow \dfrac{9}{3} = 3$
Again divide the obtained number by the smallest prime number (from which the number is divisible)
$ \Rightarrow \dfrac{3}{{3 = 1}}$
So we can write the factors as-
$ \Rightarrow \sqrt {36} = \sqrt {2 \times 2 \times 3 \times 3} $
On solving, we get-
$ \Rightarrow \sqrt {36} = 2 \times 3$
On multiplication, we get-
$ \Rightarrow \sqrt {36} = 6$

Answer- The correct answer is $6$.

Note:
Here you can also explain this question in the following way-
Since a and b are the two numbers whose product is $37$ so we can write-
$ \Rightarrow a \times b = 37$
On rearranging, we can write-
$ \Rightarrow a = \dfrac{{37}}{b}$
Now since we know that $37$ is a prime number so $b$ is equal to either $1$ or $37$ so on putting its value in the above equation, we get-
$ \Rightarrow $ If a$ = 1$ then b$ = 37$ or if $a = 37$ then b=$1$
Now, we can easily find the difference between the two numbers and solve the question further as we have done in the above solution.