Melodious
  • Melodious
which is smaller 5 root 10 or 4 root 9?????????
Mathematics
  • Stacey Warren - Expert brainly.com
Hey! We 've verified this expert answer for you, click below to unlock the details :)
SOLVED
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
jamiebookeater
  • jamiebookeater
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
anonymous
  • anonymous
You mean \(5\sqrt{10}\) or \(4\sqrt{9}\)? Observe that \(5>4\) and \(\sqrt{10}>\sqrt{9}\). Which do you think is larger?
Melodious
  • Melodious
4 root 9 is larger right?
anonymous
  • anonymous
No. Since 4<5 and sqrt9 < sqrt10, one would expect that 4sqrt9<5sqrt10, otherwise one would violate some variant of Archimedes' principle.

Looking for something else?

Not the answer you are looking for? Search for more explanations.

More answers

Melodious
  • Melodious
can u simplify the roots and help me out @nettle404
anonymous
  • anonymous
I think \(\sqrt{10}\) is about as simple as it can get. On the other hand, what squared gives you \(9\)?
Melodious
  • Melodious
3
anonymous
  • anonymous
Exactly, so \(\sqrt9=3\). But \(\sqrt{10}\) has no simple expression.
Melodious
  • Melodious
but the question is 4 root 9 so it means 4 multiplied by root 9
Melodious
  • Melodious
which is 3x4=12
anonymous
  • anonymous
Yep.
anonymous
  • anonymous
You got it.
Melodious
  • Melodious
what about 5 root 10?
anonymous
  • anonymous
Not easily simplified. Can you think of any way to square a number to obtain 10?
zepdrix
  • zepdrix
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\[\large\rm 4\sqrt9\lt5\sqrt{10}\]
zepdrix
  • zepdrix
Maybe that's more complicated though :3 lol
anonymous
  • anonymous
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.

Looking for something else?

Not the answer you are looking for? Search for more explanations.