Question

Is square root of four hundred rational or irrational? Explain your reasoning.

Answer 1

I think its irrational

Answer 2

Do you know how to find the prime factors of 400?

Answer 3

Square root of 400 is 20, since 20 x 20 is 400.
And 20 is certainly rational since it can be expressed as a fraction using integers
20 = 20/1

Answer 4

Now that you have the answer, let's figure out how you do it.
Do you know how to find the prime factors of 400?

Answer 5

??????????

Answer 6

Do you know what prime numbers are?

Answer 7

Yea

Answer 8

Every integer greater than 1 is either a prime number or a product of prime numbers.

Answer 9

I personally wouldn't bother with prime factors on thisone. When you see 400, you should think what squared equals 400? 2x2=4 and there are 2 0's so, try 20x20..hey it works. Faster than prime factorisation.

Answer 10

For example, 2, 3, 5, 7, 11 are prime numbers.
6 is not a prime number since 6 = 2 * 3, a product of prime numbers.

Answer 11

To find the prime factorization of a number, divide the number by each prime number starting with 2 as many times as possible. When it is no longer divisible by 2, move on to 3. Keep going until you get 1.

Answer 12

Ok im getting it so far

Answer 13

Here it is with 400.
400/2 = 200
200/2 = 100
100/2 = 50
50/2 = 25
25 is not divisible by 2, so we move to 3. 25 is also not divisible by 3, so we move to 5.
25/5 = 5
5/5 = 1
Since we finally got 1, the factorization is done.
Now we see what it is.
Now look at the prime numbers we divided by:
2, 2, 2, 2, 5, 5
Those numbers are the prime factorization of 400.
In other words, 400 = 2 * 2 * 2 * 2 * 5 * 5 = 2^4 * 5^2