Problem Solving #3

**matgrl** · November 2nd 2010, 05:30 PM

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?

**Wilmer** · November 2nd 2010, 06:06 PM

Use calculator.

**mr fantastic** · November 2nd 2010, 06:46 PM

Originally Posted by matgrl

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?

Without knowing the background to this question, post #2 is all you can reasonably expect to get ....

**matgrl** · November 3rd 2010, 05:42 AM

I am not allowed to. I obviously know which one is bigger using a calculator. This is problem solving

**matgrl** · November 3rd 2010, 05:43 AM

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.

**Soroban** · November 3rd 2010, 08:09 AM

Hello, matgrl!

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

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

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

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

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

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

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

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

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

**matgrl** · November 3rd 2010, 02:28 PM

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?

**Wilmer** · November 3rd 2010, 04:14 PM

Originally Posted by matgrl

How exactly does the 4 square root of 33 = 528?

Look again at what was done: 4SQRT(33) was squared;
4 squared = 16; SQRT(33) squared = 33 : 16 * 33 = 528

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