Find the positive square roots by factors method of 10816

Question

Find the positive square roots by factors method of 10816

Answer 1

2 * 5404

4 * 2704
4 * 4 * 676
4 * 4 * 4 * 169
4 * 4 * 4 * 13 * 13

sqrt of that is
2 * 2 * 2 * 13

which is 104

Answer 2

hy mam hira

Answer 3

I am not saticfied

Answer 4

2*5404

4*2704
4*4*676
4*4*4*169
4*4*4*13*13

Answer 5

Well, well, well, let's clown around with finding the positive square roots of 10816 using the factors method!

To begin, let's find the prime factors of 10816.

10816 is even, so let's divide it by 2:
10816 ÷ 2 = 5408

5408 is even as well, so let's keep dividing by 2:
5408 ÷ 2 = 2704

We're getting there! Let's keep dividing:
2704 ÷ 2 = 1352

And one more:
1352 ÷ 2 = 676

Now, let's see what else we can divide 676 by:
676 ÷ 2 = 338

Still not done, let's divide:
338 ÷ 2 = 169

Almost there! Let's divide once more:
169 ÷ 13 = 13

Ah, we found an odd prime number! And it looks like a square. So the factors method tells us that:
√10816 = √(2^6 * 13^2) = √(2^3 * 13)^2

Simplifying this expression, we obtain the positive square root:
√10816 = 2^3 * 13

So, drumroll, please... the positive square root of 10816 is 104! Ta-da!

Answer 6

To find the positive square roots of 10816 using the factors method, follow these steps:

Step 1: Prime factorize 10816
To prime factorize 10816, divide it by its smallest prime factor, which is 2:
10816 ÷ 2 = 5408

5408 is still an even number, so divide it by 2 again:
5408 ÷ 2 = 2704

Continue dividing by 2 until you can no longer divide evenly:
2704 ÷ 2 = 1352
1352 ÷ 2 = 676
676 ÷ 2 = 338
338 ÷ 2 = 169

Now, you have reached the smallest prime factor, which is 13. Divide by 13:
169 ÷ 13 = 13

Since 13 is a prime number, we have fully prime factorized 10816 as:
2 × 2 × 2 × 2 × 13 × 13 = 2^4 × 13^2

Step 2: Create pairs of equal factors
Now, create pairs of equal factors using the prime factors:
2 × 2 = 2^2
13 × 13 = 13^2

Step 3: Calculate the square roots
The square root of a number is obtained by taking the square root of each of its prime factors.

So, the positive square roots of 10816 are:
√(2^2) = 2
√(13^2) = 13

Therefore, the positive square roots of 10816 are 2 and 13.