Why is √5 smaller than 2.24, and 2.25?

Question

I did was arrange these from least to the greatest.

my anwser: 2.24,2.25,√5

correct answer: √5,2.24,2.25

My anwser SHOULD be correct, because nothing can go into √5 besides 5. And 5 is a whole #. Why is √5 the smallest?

THIS IS WITHOUT A CALCULATOR LOL

Answer 1

First of all, 5 does not "go" into √5
Secondly this has nothing to do with which number is largest.
√5 = 2.236...
2.24^2 = 5.0176 > 5

Answer 2

I thing maybe your confusion is because you don't understand the meaning of √5.

This means, the square root of 5. It means, what number, multiplied by itself, gives 5?

2 * 2 is 4
2.23 * 2.23 is a little less than 5.
2.24 * 2.24 is a little more than 5.
...
3 * 3 is 9.

Hope this helps?
.

Answer 3

Because sqrt(5) ≈ 2.23607, and 2.23607 is less than 2.24

The square root of a number can be positive or negative, so sqrt(5) ≈ -2.23607, so that is definitely less than 2.24.

Answer 4

If you put radical 5 into a calculator, it's decimal value is 2.236067977. Therefore, it is less than both 2.24 and 2.25.

Answer 5

Well, √5 is a little more than 2.236(ish), so √5 is less than 2.24

Answer 6

well.... ,√5 = x and x times x = 5...
but 2.24 times 2.24 = 5.0176 (bigger than 5)
and 2.25 times 2.25 = 5.0625 (also bigger than 5)

sooo.... ,√5 is smaller than 2.24 and 2.25

Answer 7

Why are you trying to GUESS what the value of √5 is? The rest of the world uses a calculator or even (in my day) works it out by hand...............

Answer 8

(√5)² = 5
2.24² = 5.0176 > 5
2.25² = 5.0625 > 5
Thus (√5)² is the smallest.