Question

How do you find square root $5625$?

Answer 1

Hint:
There are various methods that we can use for finding the square root of any number but the easiest and useful method is factoring by squares in which we split a given number into the prime factor and make a square of every prime number.

Complete step by step Solution:
According to the question we need to find the square root of $5625$
So, we will split it into prime numbers factor, now we will factorize it
We know that all numbers have their last digit as an odd number like $(1,2,3,4,.........)$ and we also know about the divisibility rules if any number’s last digit is $5$ and $0$ then it divided by the $5$ so now we will divide our given number by $5$ because our number is $5625$ in which the last digit is $5$
Now after dividing $5625$ by $5$ we will get $1125$
$ \Rightarrow 5625 = 5 \times 1125$
Now again we get $1125$ which is also divisible by the $5$ after dividing we will get $225$
$ \Rightarrow 5625 = 5 \times 5 \times 225$
Now again we get $225$ which is also divisible by the $5$ after dividing we will get $45$
$ \Rightarrow 5625 = 5 \times 5 \times 5 \times 45$
Now again we get $45$ which is also divisible by the $5$ after dividing we will get $9$
$ \Rightarrow 5625 = 5 \times 5 \times 5 \times 5 \times 9$
Now we know that $9$ is the square of $3$that is $3 \times 3 = 9$
So, our number is factorizing and after factorizing our number is in the prime factor and we get
$ \Rightarrow 5625 = 5 \times 5 \times 5 \times 5 \times 3 \times 3$
Now we can see in the above equation we have a pair of each prime number now we can write it as
$ \Rightarrow 5625 = {(5 \times 5 \times 3)^2}$
So, our square root of $5625$ is the $(5 \times 5 \times 3) = 75$ which is the required answer to our question

Therefore the square root of $5625$ is $75$ which is our required answer.

Note:
We can solve it very quick in just two-step if use this method our given number is $5625$ so our number’s last two digit is $25$ which is square of $5$ that is ${5^2} = 25$ so our square root numbers
The last digit is $5$ now our numbers starting two digit we will factorize it in the form of $n(n + 1)$ where $n$ is our square root’s starting digit for example in our given number $5625$ two starting digits are $56$ we can factorize it in $7(7 + 1)$ where $n = 7$ which is our square root’s starting digit so our square root of $5625$ is $75$.