Question

Find the square root of 400 by Prime Factorization Method.

Answer 1

Hint: Start dividing 400 by the smallest prime number by which it is divisible. List all such prime numbers and write them in the form of $a\times b\times c\times d\times e.......$, where a, b, c, d, e…… are the prime numbers which divide 400. Now, form pairs of multiplication of similar numbers such that all the prime numbers are paired and no prime number is left. To find the square root, take one factor from each pair and multiply them together.

Complete step-by-step answer:
Prime numbers are the numbers that have only two factors. One factor is 1 and the other is the number itself.
Let us come to the question. Let us list the prime numbers by which 400 is divisible. So, 400 is divisible by only two prime numbers, they are 2 and 5. Now, writing 400 as the product of its prime factors, we get,
$400=2\times 2\times 2\times 2\times 5\times 5$
Now, forming pairs of similar numbers, we have,
$400=\left( 2\times 2 \right)\times \left( 2\times 2 \right)\times \left( 5\times 5 \right)$
Taking one prime number from each pair, we get,
$2\times 2\times 5$
Multiplying these numbers together, we get 20.
Hence, 20 is the square root of 400.

Note: One may note that we have to break the number into its prime factors only and not in composite factors. For example: 10 is also a factor of 400 but if we will break 400 in such composite factors then we will not get a clear idea about the square root as we will not be able to form pairs. Although, in some cases we will be able to form pairs of composite factors also but it is preferable to break the number into its primes.