Question

Find the square root of $ 1600 $ .
(A) $ 40 $
(B) $ 20 $
(C) $ 10 $
(D) None of these

Answer 1

Hint: To find the square root of the given number $ 1600 $ , we will use prime factorisation method. We will write that number as the multiple of the primes. After that it will be written in the form of a group of two. Then, we will select one prime number from each group and multiply all such prime numbers. The square root of $ 1600 $ will be the product of selected prime numbers.

Complete step-by-step answer:
To solve the given problem, we must know the prime factorisation method. By using the method of prime factorisation, we can express the given number as a product of prime numbers. Therefore, we will write the given number $ 1600 $ as the product of primes. Let us do prime factorisation of $ 1600 $ . Note that here $ 1600 $ is an even number so we can start prime factorisation with prime number $ 2 $ .

$ 2 $	$ 1600 $
$ 2 $	$ 800 $
$ 2 $	$ 400 $
$ 2 $	$ 200 $
$ 2 $	$ 100 $
$ 2 $	$ 50 $
$ 5 $	$ 25 $
$ 5 $	$ 5 $
	$ 1 $

Therefore, we can write $ 1600 = 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 5 \times 5 $ .
Now we will take the same prime numbers together and write them in groups of two as shown below.
 $ 1600 = \left( {2 \times 2} \right) \times \left( {2 \times 2} \right) \times \left( {2 \times 2} \right) \times \left( {5 \times 5} \right) $
Now we will take one number from each group. Therefore, we will get $ 2,2,2 $ and $ 5 $ from the first, second, third and fourth group respectively. Hence, the square root of $ 1600 $ will be the product of these numbers $ 2,2,2 $ and $ 5 $ .
Therefore, $ \sqrt {1600} = \sqrt {{2^2} \times {2^2} \times {2^2} \times {5^2}} $
 $ \Rightarrow \sqrt {1600} = 2 \times 2 \times 2 \times 5 $
 $ \Rightarrow \sqrt {1600} = 40 $
Therefore, the square root of $ 1600 $ is $ 40 $ . Hence, option A is correct.
So, the correct answer is “Option A”.

Note: If the number is even then it is divisible by $ 2 $ . If the sum of all digits of a number is divisible by $ 3 $ then that number is divisible by $ 3 $ . If the unit digit of the number is either $ 0 $ or $ 5 $ then that number is divisible by $ 5 $ . To find the cube root, we will write the number as the multiple of the primes. After that it will be written in the form of a group of three. Then, we will select one prime number from each group and multiply all such prime numbers.