Are the two numbers

square root of 3 + and square root of 11 and

square root of 5 + square root of 8 equal? If not, which is larger?

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- Nov 2nd 2010, 05:30 PMmatgrlProblem Solving #3
**Are the two numbers**

square root of 3 + and square root of 11 and

square root of 5 + square root of 8 equal? If not, which is larger?

- Nov 2nd 2010, 06:06 PMWilmer
Use calculator.

- Nov 2nd 2010, 06:46 PMmr fantastic
- Nov 3rd 2010, 05:42 AMmatgrl
I am not allowed to. I obviously know which one is bigger using a calculator. This is problem solving

- Nov 3rd 2010, 05:43 AMmatgrl
I know I need to set an equation making these vairbales equal to each other. Then I need to square this equation but this is all I know.

- Nov 3rd 2010, 08:09 AMSoroban
Hello, matgrl!

Quote:

$\displaystyle \text{Are the two numbers }\sqrt{3} + \sqrt{11}\,\text{ and }\,\sqrt{5} + \sqrt{8}\,\text{ equal?}$

$\displaystyle \text{If not, which is larger?}$

We have: . . . .$\displaystyle \sqrt{3} + \sqrt{11} \quad[?]\quad \sqrt{5} + 2\sqrt{2}$

Square: . .$\displaystyle 3 + 2\sqrt{33} + 11 \quad [?]\quad 5 + 4\sqrt{10} + 8 $

. . . . . . . . . . . $\displaystyle 1 + 2\sqrt{33} \quad [?] \quad 4\sqrt{10}$

Square: .$\displaystyle 1 + 4\sqrt{33} + 132 \quad [?]\quad 160$

. . . . . . . . . . . . . .$\displaystyle 4\sqrt{33} \quad[?]\quad 27 $

Square: . . . . . . . . . $\displaystyle 528 \quad[?]\quad 729$

Since 528 < 729, the original statement is: .$\displaystyle \sqrt{3} + \sqrt{11} \;<\;\sqrt{5} + \sqrt{8}$

- Nov 3rd 2010, 02:28 PMmatgrl
This is great! Once again thank you :)

I have a question on the way you did your square roots. How exactly does the 4 square root of 33 = 528? I am not sure how to do this...could you show me? - Nov 3rd 2010, 04:14 PMWilmer