Question

which is smaller 5 root 10 or 4 root 9?????????

Answer 1

You mean \(5\sqrt{10}\) or \(4\sqrt{9}\)? Observe that \(5>4\) and \(\sqrt{10}>\sqrt{9}\). Which do you think is larger?

Answer 2

4 root 9 is larger right?

Answer 3

No. Since 4<5 and sqrt9 < sqrt10, one would expect that 4sqrt9<5sqrt10, otherwise one would violate some variant of Archimedes' principle.

Answer 4

can u simplify the roots and help me out @nettle404

Answer 5

I think \(\sqrt{10}\) is about as simple as it can get. On the other hand, what squared gives you \(9\)?

Answer 6

3

Answer 7

Exactly, so \(\sqrt9=3\). But \(\sqrt{10}\) has no simple expression.

Answer 8

but the question is 4 root 9
so it means 4 multiplied by root 9

Answer 9

which is 3x4=12

Answer 10

Yep.

Answer 11

You got it.

Answer 12

what about 5 root 10?

Answer 13

Not easily simplified. Can you think of any way to square a number to obtain 10?

Answer 14

You can introduce another number like this if it helps you understand what is going on.

\[\large\rm 4\sqrt9\lt5\sqrt9\]But also\[\large\rm 5\sqrt9\lt5\sqrt{10}\]So we see that\[\large\rm 4\sqrt{9}\lt5\sqrt9\lt5\sqrt{10}\]Therefore\[\large\rm 4\sqrt9\lt5\sqrt{10}\]

Answer 15

Maybe that's more complicated though :3 lol

Answer 16

How about proof by contradiction?

Suppose that \(5\sqrt{10}\leq4\sqrt{9}\), then \(5\sqrt{10}\leq12\) and \(\sqrt{10}\leq12/5\). Since \(\sqrt{10}>3\) but \(12/5<3\), we have \(3<3\), which is false.