Find the square root by prime factorization method of 1156.

To find the square root of 1156 using the prime factorization method, we first need to break down the number into its prime factors.

Step 1: Prime Factorization

We start by dividing 1156 by the smallest prime number, which is 2:

• 1156 ÷ 2 = 578
• 578 ÷ 2 = 289

Next, we factor 289:

• 289 ÷ 17 = 17
• 17 ÷ 17 = 1

Thus, the prime factorization of 1156 is:

2 × 2 × 17 × 17 or 2² × 17².

Step 2: Finding the Square Root

To find the square root, we take one of each pair of prime factors:

• From 2², we take 2.
• From 17², we take 17.

Now, we multiply these results:

2 × 17 = 34.

Final Result

The square root of 1156 is 34.