Question

How do you write $\sqrt {125} $ in simplified radical form?

Answer 1

Hint:There are various methods which 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. But here we have to write it in the simplified radical form.

Complete step by step Solution:
According to the question we need to write $\sqrt {125} $ in the simplified radical form for we will use the same process as finding the square roots of any number.
So, we will split $125$ into prime numbers factor, now we will factorize it
We know that all numbers have its 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 is 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 $125$ by $5$ we will get $25$
$ \Rightarrow 125 = 5 \times 25$
Now again we get $25$ which is also divisible by the $5$ after dividing we will get $5$
$ \Rightarrow 125 = 5 \times 5 \times 5$
So, our number is factoring and after factoring our number is in the prime factor and we get
$ \Rightarrow 125 = 5 \times 5 \times 5$
Now we can see in the above equation we have one pair of $5$ but the one $5$ is in the single form so it will remain in the square root as $\sqrt 5 $ now we can write it as
$ \Rightarrow \sqrt {125} = \sqrt {(5 \times 5) \times 5} $
And after solving it we will get $\sqrt {125} = 5\sqrt 5 $
So, our simplified radical form of the $\sqrt {125} $ is the $5\sqrt 5 $ which is the required answer to our question.

Therefore the simplified radical form of the $\sqrt {125}$ is the $5\sqrt 5$ which is our required answer.

Note: There is no other method that is simple compared to this method. We have to solve our above question by this method because this method is very easy and quick and it is the basic if we want to solve any question then for any other question you can use it as it is.