Prove that it is smaller than 6

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Homework Help Overview

The discussion revolves around a proof involving inequalities, specifically demonstrating that a certain expression is smaller than 6. The subject area appears to involve algebraic manipulation and properties of square roots.

Discussion Character

  • Exploratory, Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • Participants discuss various methods for proving the inequality, including squaring both sides of the expression and evaluating square roots. Some express confusion about the steps involved and seek clarification on how to proceed after certain manipulations.

Discussion Status

There are multiple attempts to approach the problem, with participants sharing their reasoning and questioning the validity of their steps. Some guidance has been offered regarding the manipulation of square roots and squaring expressions, but no consensus has been reached on the best method to prove the statement.

Contextual Notes

Participants mention the positivity of both sides of the inequality as a relevant constraint in their reasoning. There is also a note about the potential complexity of the expressions involved, which may affect the clarity of the proof.

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Homework Statement



Prove that
MSP340419h1i98721f4618g000016f428dc98cfg230.gif
.


Homework Equations





The Attempt at a Solution



I couldn't prove this... Can anyone help me? Thanks...
 
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Michael_Light said:

Homework Statement



Prove that View attachment 38334.


Homework Equations





The Attempt at a Solution



I couldn't prove this... Can anyone help me? Thanks...


Since both sides are positive take squares of them
 
stallionx said:
Since both sides are positive take squares of them

By squaring both sides, i stuck at sqrt20 < 4.5 , how do i proceed?

stallionx said:
You'll end up 81>80

Sorry but i can't get you...
 
If you directly go by solving the square roots of 10 and 2, what you get is something 5.99 which is less than 6. :smile:
 
Michael_Light said:
By squaring both sides, i stuck at sqrt20 < 4.5 , how do i proceed?
Square both sides again. That is, square 4.5 and show that it is equal to 20.25

It would probably look a bit nicer though if you left it as [itex]2 \sqrt{20} < 9[/itex] before squaring.
 

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