Question

What’s the square root of $625$?

Answer 1

Hint: In this question we have been given with the number $625$ and we have to find the square root of the given number. We will use the method of prime factorization to get the required solution. We will first write the number $625$ in terms of the multiplication of its prime numbers and then we will multiply a single term if there are $2$ instances of it in multiplication. After removing the terms from the square root, we will multiply them to get the required solution.

Complete step-by-step solution:
We have the number given to us as:
$\Rightarrow 625$
Since we have to find its square root, the number can be written as:
$\Rightarrow \sqrt{625}$
Now we know that the number $625$ is divisible by $5$ and it can be written as $5\times 125$ therefore, on substituting, we get:
$\Rightarrow \sqrt{5\times 125}$
Now we know that the number $125$ is divisible by $5$ and it can be written as $5\times 25$ therefore, on substituting, we get:
$\Rightarrow \sqrt{5\times 5\times 25}$
Similarly, the number $25$can be written as:
$\Rightarrow \sqrt{5\times 5\times 5\times 5}$
Now we can see that there are $4$ instances of the number $5$ in the square root. On writing in the exponent form, we get:
$\Rightarrow \sqrt{{{5}^{4}}}$
Now since we have to take the square root it implies that we consider half the exponent therefore, the number becomes:
$\Rightarrow {{5}^{2}}$
On simplifying, we get:
$\Rightarrow 25$, which is the square root.
Therefore, $\sqrt{625}=25$ is the required solution.

Note: It is to be noted that we have solved this question by the prime factorization method, there also exists other methods such as the repeated subtraction method. It is to be noted that when in square root, the negative of the square root is also a square root. In this case $-25$ is also square root $625$ because of multiplying $-25\times -25=625$, since multiplication of two negatives gives a positive number.