Find the square roots of the numbers by expressing each number as the product of primes :
169

Answer

To find the square root of 169 by expressing it as the product of primes, we will follow these steps:

### Step 1: Prime Factorization of 169
First, we need to factor the number 169 into its prime factors. The smallest prime number is 2, but 169 is not divisible by 2. The next prime number is 3, and 169 is also not divisible by 3.

Next, we check 5, which also does not divide 169. The next prime number is 7, which again does not divide 169. Finally, we check 11, and then we check 13.

When we divide 169 by 13:
\[ 169 ÷ 13 = 13 \]
So, we can express 169 as:
\[ 169 = 13 × 13 \]
Thus, the prime factorization of 169 is:
\[ 169 = 13^2 \]

### Step 2: Finding the Square Root
Now that we have the prime factorization, we can find the square root of 169. The square root of a number is found by taking one factor from each pair of the same number.

Since we have:
\[ 169 = 13 × 13 \]
We can take one 13 from the pair:
\[ \sqrt{169} = \sqrt{13 × 13} = 13 \]

### Final Answer
Thus, the square root of 169 is:
\[ \sqrt{169} = 13 \]

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