Question

What is the square root of 42?

Answer 1

Hint: We are given with a number. We have to find the root of that number. So we will take help of the prime factors method for this solution. We will try to factor the number in the form of a product of prime numbers and will try to find any perfect square there is inside the root.

Complete step-by-step answer:
Given the number is 42.
Now we will write the number in the root form.
\[\sqrt {42} \]
Now factorise this in the form of prime numbers.
\[ = \sqrt {2 \times 21} \]
Now divide 21 in the form of a product of prime numbers.
\[ = \sqrt {2 \times 3 \times 7} \]
Now all the numbers inside the root are prime but there is no such perfect square number. So we can conclude that the root of 42 is \[\sqrt {42} \] only.
So, the correct answer is “ \[\sqrt {42} \] ”.

Note: Note that if the number after splitting into factors of prime numbers and we get a perfect square there then we can take it out of the root but in the case above we are unable to do that so we can directly write the number inside the root.
Also if we are given the value of the square root of 2, 3 and 7 then their product will give the value of \[\sqrt {42} \].
\[\sqrt {42} = \sqrt 2 \times \sqrt 3 \times \sqrt 7 \]