Question

Find the square root of 1156
A. 34
B. 54
C. 61
D. 21

Answer 1

Hint: As a square root of a number $y$ is a number $x$ such that ${{x}^{2}}=y$. In this question try to write the given number as prime factors. So here write the given number as $N={{2}^{a}}{{3}^{b}}{{5}^{c}}...$ that is in power of prime numbers. square root is a number that, when multiplied by itself, gives the original number.

Complete step-by-step answer:
We have to find out the square root of 1156, so in order to find out square root of 1156 we have to find out the prime factor of 1156
So, we can factorise 1156 as
$\begin{align}
  & 1156=2(578) \\
 & 578=2(2)(289) \\
\end{align}$
Now we have to factorise 289, so we can write further
$289=(17)(17)$
Hence, we can write the factors of 1156 as
\[\begin{align}
  & 1156=(2)(2)(17)(17) \\
 & \Rightarrow 1156={{\left( 2 \right)}^{2}}{{\left( 17 \right)}^{2}}----(a) \\
\end{align}\]
Now suppose square root of $1156$ is N
So as per definition we can write from equation $(a)$
${{N}^{2}}=1156$
So, in prime factors we can write
\[\begin{align}
  & {{N}^{2}}={{(2)}^{2}}{{(17)}^{2}} \\
 & \Rightarrow N=(2)(17) \\
 & \Rightarrow N=34 \\
\end{align}\]
So, the square root of 1156 is 34, Hence, option A is correct.

Note: We can also find the square root of a number by long division method .It should be noted here every positive number $x$ has two square roots:$\sqrt{x}$ , which is positive, and $-\sqrt{x}$ which is negative. In this question we have to select the positive value of square root. In real numbers the square root of a negative number is not defined.