# Math Help - Problem Solving #3

1. ## Problem 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?

2. Use calculator.

3. 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 ....

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

5. 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.

6. 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: . $\sqrt{3} + \sqrt{11} \;<\;\sqrt{5} + \sqrt{8}$

7. 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?

8. 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