Question

Find the square root of a number 8100 by Prime Factorization Method.

Answer 1

Hint- The factors of a number are the divisor which will completely divide the number without
leaving any remainder. To find the square root of a number by prime factorization method, first divide
the given number to its prime factor then make the pair of similar factor, so that factor in each pair is
equal then square root all the pair of factor and find the product of factor. The square root of a number
is a number whose square is equal to the original number. The numbers which are divisible by 1 and by
itself only, i.e., it should have only two factors is known as Prime numbers.
Complete step by step solution:
The prime factors of a number should be such that the multiplication of all the prime factors results in
the number itself.
The first prime number is 2. So, divide 8100 by 2 gives 4050 as the quotient and 0 as remainder.
Similarly, divide 4050 again by 2, we get 2025 as quotient.
Now, 2025 is not divisible by 2 exactly, so divide 2025 by another higher prime number i.e., 3 which
gives 675 as quotient.
Again, divide 675 by 3, we get 225 as quotient.
Again, divide 225 by 3, we get 75 as quotient.
Again, divide 75 by 3, we get 25 as quotient.
Now, 25 is not divisible by 3 so; we look for another higher prime number which should divide 25
exactly.
So, divide 25 by 5, we get 5 as quotient and 0 as remainder.
In total, we can write,
$8100 = \left[ {2 \times 2} \right] \times \left[ {3 \times 3} \right] \times \left[ {3 \times 3} \right] \times
\left[ {5 \times 5} \right]$
Group the numbers which are coming two times as weed to find out the square root.
*In case of cube root, we group for the number which comes thrice.
Now, multiply each element of the group once to determine the result.
$\sqrt {8100} = 2 \times 3 \times 3 \times 5 = 90$
Hence, the square root of 8100 is 90.
Note: Always find the prime factor of the number and group them into the pairs of similar factors.
Another way of determining the square root of a number is by long division method, which is more
complex, and the chances of getting errors are more.