Evaluate the square root of 1156 by prime factorization

We have to find the square root of 1156 by prime factorisation

Solution

We will use prime factorisation method to find the square root

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

The first step is to divide the number 1156 with the smallest prime factor, say 2.
1156 ÷ 2 = 578
578 ÷ 2 = 289

289 ÷ 17 = 17

17 ÷ 17 = 1

Finally, we received the number 1 at the end of the division process. So that we cannot proceed further.

So, the prime factors of 1156 are written as 2 × 2 × 17 × 17

On paring the factors we get

1156= (17 x 17 ) (2 x 2)

√1156= √ (2 x 17)

√1156= 34

Answer

The square root of 1156 = 34

√1156= 34

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