Question

what is the square root of 169 by prime factorization method​

Answer 1

Answer:

$\sqrt{169 = ......}$

so

13 | 169

-----------

13 | 13

----------

| 1

----------

It means square root of 169 is 13.

Answer 2

The square root of 169 by prime factorization method is 13.

To find the square root of 169 by prime factorization method, we need to factorize 169 into its prime factors and then take the square root of each factor.

First, we check if 169 is a perfect square.

Since the square of 13 is 169, we know that 169 is a perfect square.

Next, we can factorize 169 into its prime factors.We can start by dividing it by the smallest prime number, 2.

However, 2 is not a factor of 169. Next, we try dividing by 3. 169 is not divisible by 3 either.

Next, we try 5.

Again, 169 is not divisible by 5.

Finally, we try 7. 169 is divisible by 7.

169 ÷ 7 = 24 R 1

We continue the process with 24, which is not divisible by 2 or 3, but is divisible by 2.

24 ÷ 2 = 12

Next, we try 2 again with the quotient.

12. 12 ÷ 2 = 6

Now, we try 2 again with the quotient.

6. 6 ÷ 2 = 3

Since 3 is a prime number, we stop here.

Therefore, the prime factorization of 169 is 13 × 13.

Taking the square root of each factor, we get:

√13 × √13 = 13

Therefore, the square root of 169 by prime factorization method is 13.

For similar question on prime factorization method​.

https://brainly.in/question/4486490

#SPJ3