Question

Find the square root by prime factorization method of 1156.

Answer 1

Hint – The square root of any number P is ${P^{\dfrac{1}{2}}}$. Write down all the factors of the given numbers and we are concerned about the prime factors only. Use these two concepts in togetherness to get the answer.

Complete step-by-step answer:
We have to find out the square root of 1156 using the prime factorization method.
$ \Rightarrow \sqrt {1156} = {\left( {1156} \right)^{\dfrac{1}{2}}}$……………………. (1)
So, first factorize the given number.
Therefore 1156 factorization\[{\text{ = 2}} \times 2 \times 17 \times 17\], (where, 2 and 17 is a prime number)
A number is called a prime number if the factor of the number is either 1 or itself.
So, 2 is multiplied two times and 17 is also multiplied two times together to make the original number.
$\therefore $Prime factorization of 1156\[ = {2^2} \times {17^2}\]
So substitute this value in above equation we have,
$ \Rightarrow \sqrt {1156} = {\left( {1156} \right)^{\dfrac{1}{2}}} = {\left( {{2^2} \times {{17}^2}} \right)^{\dfrac{1}{2}}}$
Now simplify the above equation we have,
$ \Rightarrow \sqrt {1156} = {\left( {{2^2} \times {{17}^2}} \right)^{\dfrac{1}{2}}} = {2^{2 \times \dfrac{1}{2}}} \times {17^{2 \times \dfrac{1}{2}}} = 2 \times 17 = 34$
So this is the required cube root using the prime factorization method.

Note – Prime factorization means finding the prime numbers which get multiplied together to form the original number. Now there is a trick to find the square root of any number without using prime factorization. First of all we need to remember all the square roots of numbers from 1 to 10, another thing that we need to remember is if the last digit of the number whose square is to find is 1, 4, 5, 6, 9 ,0 .