Question

Find the square root by prime factorization method of 1156.

Answer 1

Hint – The square root of any number P is $P^{{\displaystyle \frac{1}{2}}}$. 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.
$\Rightarrow \sqrt{1156}={\left(1156\right)}^{{\displaystyle \frac{1}{2}}}$……………………. (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,
$\Rightarrow \sqrt{1156}={\left(1156\right)}^{{\displaystyle \frac{1}{2}}}={\left(2^2\times {17}^2\right)}^{{\displaystyle \frac{1}{2}}}$
Now simplify the above equation we have,
$\Rightarrow \sqrt{1156}={\left(2^2\times {17}^2\right)}^{{\displaystyle \frac{1}{2}}}=2^{2\times {\displaystyle \frac{1}{2}}}\times {17}^{2\times {\displaystyle \frac{1}{2}}}=2\times 17=34$
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 .