Question & Answer

Find the square root of 6084 by division method.

ANSWER Verified Verified
Hint- It can be easily solved by first dividing it by prime numbers, and checking for all possible prime numbers and we will check for prime numbers more than 2 . This process will continue till we get 1 at the last.Product of these prime numbers and finding square root we will get the required square root for the given number.

Complete step-by-step answer:
According to the question, we have to find out the square root of 6048. So as mentioned above, we will follow the division till we get 1 at last.

$\therefore 2 \times 2 \times 3 \times 3 \times 13 \times 13 = 6048$
$\therefore {2^2}{.3^2}{.13^2} = 6048$, we have to calculate the square root
$\therefore \sqrt {{2^2}{{.3}^2}{{.13}^2}} = \sqrt {6048} $
$ \Rightarrow 2 \times 3 \times 13 = \sqrt {6048} = 78$
Hence, we get a square root of 6048 equals 78.

Note- This type of question based on calculation of square roots can also be calculated using a long division method as well. But long division method calculation is time taking and students might commit calculation mistakes leading to wrong answers. So students should generally prefer this method.