Prove that it is smaller than 6

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The discussion revolves around proving that a certain value is smaller than 6, with participants sharing their attempts and methods. One user suggests squaring both sides of the inequality, leading to a comparison involving square roots. Another participant points out that directly calculating the square roots yields a value slightly less than 6. Additional advice includes rearranging the expression for clarity before squaring. The conversation emphasizes various approaches to tackle the proof effectively.
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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 2 \sqrt{20} &lt; 9 before squaring.
 

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