Classwork on radicals, square roots, quadratic equations

1. Simplify $\sqrt{48}$ (hint: factor)
2. Simplify $\sqrt{18}+\sqrt{32}+\sqrt{75}$ (hint: factor, distribute)
3. Simplify $\sqrt{\frac{5}{3}}$ (hint: quotient rule, simplify fractions)
4. Solve for $x$: $x^2+9=25$ (hint: set equal to zero and factor, or not)
5. Solve for $x$: ${\left(3\sqrt{5}\right)}^2+{\left(3\sqrt{2}\right)}^2=x^2$ (square each square)

6. Solve for $x$. (Hint: get 0 on one side and factor)

   1. $x^2-10x=-16$
   2. $x^2+5x=0$

Useful properties

1. $\sqrt{ab}=\sqrt{a}\sqrt{b}$
2. $\sqrt{\frac{a}{b}}=\frac{\sqrt{a}}{\sqrt{b}}$
3. If $a^2=x^2$ then $x=\pm a$
4. Property of zero: If $ab=0$ then $a=0$ or $b=0$. This is one reason factoring is useful. For example to solve $x^2+4x+3=0$, we can factor to solve $(x+3)(x+1)=0$, which is much easier.

5. Distributive law box for multiplying and factoring:

   	$x$	$+1$
   $x$	$x^2$	$x$
   $+3$	$3x$	3