Question

How do you find the square root of$2000$?

Answer 1

Hint:
To calculate the square root student should always find out the factors of the given number. After simplifying the number in terms of its prime factors, factors that appear twice should be taken out of the square root and should be written once. In this method the student should know the factorization method to find the factors of the given number. Factorization method is important not only for finding the square root but also for finding the LCM of a given number. The last step is the repetition of the second step i.e. taking out all the common multiples and writing them once and leaving the remaining factors inside the square root.

Complete step by step solution:
First step is to find out the factors of $2000$ by factorization method.
After factorization we get the following factors of $2000$
\[\sqrt {2000} = \sqrt {20 \times 100} ......(1)\]
Further simplifying
$\sqrt {2000} = \sqrt {2 \times 2 \times 5 \times 10 \times 10} ......(2)$
We can see that $2\& 10$appear twice, thus moving them outside the square root sign. Next step is as follows
$\sqrt {2000} = 2 \times 10\sqrt 5 ......(3)$

Thus the square root of $2000$ is $20\sqrt 5 $

Note:
The student should learn this method if he/she is not acquainted with it. This method is very useful in competitive exams and also for fast and approximate calculation of the square root when the calculator is not available. For the numbers left inside the square root, he/she should take the approximate value and multiply it with the multiples whose square root is already found to find the square root of the number given in the question.