Question

Evaluate the square root of $1156$ by prime factorization

Answer 1

The number $1156$ is a composite and it should have prime factors. Now let us know how to calculate the prime factors of $1156$.

Step 1

Prime factorizing given number

The first step is to divide the number $1156$ with the smallest prime factor, say $2$ and then by other factors till we get $1$

$$\begin{gathered} 1156÷2=578 \\ 578÷2=289 \\ 289÷17=17 \\ 17÷17=1 \end{gathered}$$

So

$1156=2\times 2\times 17\times 17$

Step 2

Finding square root by pairing the factors

$$\begin{gathered} \Rightarrow \sqrt{1156}=\sqrt{(2\times 2)\times (17\times 17)} \\ \Rightarrow \sqrt{1156}=2\times 17=34 \end{gathered}$$

Hence the square root of $1156$ is $34$