8.2 Some very important generalizations

$\sqrt{9}=$

$\sqrt{4}=$

$\sqrt{9}\times \sqrt{4}=$

$\sqrt{9\times 4}$

Based on #1-4, write an algebraic generalization.

Now, give me a completely different example of that same generalization: four different statements, like #1-4, that could be used to generate that same generalization.

$\frac{\sqrt{9}}{\sqrt{4}}=$

$\sqrt{\frac{9}{4}}$

• A

  What do you think is the answer?

• B

  Test by squaring back. (To square anything, multiply it by itself. So this just requires multiplying fractions!) If it doesn’t work, try something else, until you are convinced that you have a good [xxx].

Based on exercises #7-8, write an algebraic generalization.

$\sqrt{9}+\sqrt{4}=$

$\sqrt{9+4}$

Based on exercises #10-11, write an algebraic generalization that is not true.