Square root with larger answer?

Question

Please help! I'm so exhausted and have a lot of homework to do. I need help with one of my Geometry questions

I have to find a counterexample for

"The Square root of a number x is always less than x"

and

"If the product of two numbers is even, then the two numbers must be even"

I know they probably pretty easy, but I just can't think straight I'm so tired!

Answer 1

There is an infinity of counterexamples.  Try two:

The square root of 1/4 is ?

2 x 3 (an odd number) is ?

Answer 2

The first one...you're not thinking outside the box, you're only thinking of big numbers, think smaller!

The second one...how else can you get an even number when you multiply two numbers?  They want you to not use two even numbers, so try a different option.