Find the square roots of the numbers by expressing each number as the product of primes :
676

Answer

To find the square root of 676 by expressing it as the product of primes, we will follow these steps:

### Step 1: Prime Factorization of 676
We start by dividing 676 by the smallest prime number, which is 2.

- 676 ÷ 2 = 338
- 338 ÷ 2 = 169

Now, we can no longer divide by 2 since 169 is not even. We move to the next smallest prime number, which is 3.

- 169 is not divisible by 3, so we try the next prime number, which is 5.
- 169 is also not divisible by 5, so we try 7.
- 169 is not divisible by 7, so we try 11.
- 169 is not divisible by 11, so we try 13.

- 169 ÷ 13 = 13
- 13 ÷ 13 = 1

Now we have completed the factorization. The prime factors of 676 are:
\[ 676 = 2 \times 2 \times 13 \times 13 \]

### Step 2: Grouping the Prime Factors
Next, we group the prime factors into pairs:
- (2, 2) and (13, 13)

### Step 3: Taking the Square Root
When taking the square root, we take one number from each pair:
- From the pair (2, 2), we take 2.
- From the pair (13, 13), we take 13.

Now we multiply these together:
\[ \sqrt{676} = 2 \times 13 = 26 \]

### Final Answer
Thus, the square root of 676 is:
\[ \sqrt{676} = 26 \]

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