Question

Find the square root of a prime number 1096 by Prime Factorization Method.

Answer 1

Hint – Here we will proceed, using the method of prime factorization that is we repeat the process again till we get the prime factors of all composite numbers.

Complete step-by-step answer:

We have to find the square root of prime number 1096 by Prime Factorization Method.
1096 is a composite number.
Prime factorization: 1096 = 2 $ \times $2 $ \times $ 2 $ \times $ 137, which can be written 1096 = ${2^3} \times 137$
The exponents in the prime factorisation are 1 and 3. Adding one to each and multiplying we get (3+1) (1+1) = 4 $ \times $ 2 = 8. Therefore 1096 has exactly 8 factors.
Factors of 1096: 1,2,4,8,137,274,548,1096
Factor pairs: 1096 = 1$ \times $1096, 2$ \times $548, 4$ \times $ 274, or 8$ \times $ 137
Taking the factor pair with the largest square number factor, we get
 $
  \sqrt {1096} = \left( {\sqrt 4 } \right)\left( {\sqrt {274} } \right) \\
   = 2\sqrt {274} \\
   = 33.10589 \\
 $

Note – Whenever we come up with this type of problem, one can easily solve factorisation by using various methods that are upside down division, factorisation by substitution. By these basics one can easily solve this question. (Here Prime Factorisation).