Question

Find the square root of 8100 by prime factorization method.
A. 80
B. 90
C. 30
D. 70

Answer 1

Hint: In order to solve this problem we need to find the square root of 8100 by multiplying only the prime numbers in pairs. Prime numbers are those numbers which have only two factors : 1 and the number itself. Knowing this will solve your problem and will give you the right answer.

Complete step by step answer:
We need to find the square root of 8100 by prime factorisation method.
Prime factorisation method: The method of prime factorization is used to “break down” or express a given number as a product of prime numbers. More so, if a prime number occurs more than once in the factorization, it is usually expressed in exponential form to make it look more compact.
Square root of a number is that one number such that if we multiply it twice we get that number. For example 4 is the square root of 16.
We can right 8100 in terms of prime numbers as:
8100 = 5 x 5 x 3 x 3 x 3 x 3 x 2 x 2.
All the numbers present above are prime numbers 2, 3, 5.
On taking square root of both sides we get,
$$\sqrt{8100}=\sqrt{5\times 5\times 3\times 3\times 3\times 3\times 2\times 2}$$
It can also be written as $\sqrt{8100}=\sqrt{5^2\times 3^2\times 3^2\times 2^2}=5\times 3\times 3\times 2=90$.
Hence, the square root of 8100 is 90.

So, the correct answer is “Option B”.

Note: In these types of questions we must know that in mathematics, a square root of number x is a number y such that square of y is equal to x. All non-zero numbers have only one real root. The method of prime factorization is used to “break down” or express a given number as a product of prime numbers. More so, if a prime number occurs more than once in the factorization, it is usually expressed in exponential form to make it look more compact.