Warm Up Solutions

Simplify.

$\sqrt{- 54}$

$\sqrt{- 1 \cdot 2 \cdot 3^{3}} i \cdot 2^{\frac{1}{2}} \cdot 3^{\frac{3}{2}} 3 i \sqrt{2 \cdot 3}$

$3 i \sqrt{6}$

Note

Q: What is the classification for the simplified expression?
A: Complex number 

Q: Why can you simplify the square root of a negative number now (but you were not before)?
A: Because now I know that the square root of –1 is the imaginary number i.

$\sqrt{- 121}$

$\sqrt{- 1 \cdot 11^{2}}$

11i

Factor completely.

$3 x^{2} - 27$

$3 (x^{2} - 9)$

$3 (x + 3) (x - 3)$

$- 2 x^{3} - 20 x^{2} - 50 x$

$- 2 x (x^{2} + 10 x + 25)$

$- 2 x (x + 5) (x + 5) or - 2 x {(x + 5)}^{2}$

Note

Q: What is the first step in factoring?

A: Checking for and factoring out the greatest common factor, GCF

Q: What is the classification of the expression in problem 4 by degree and number of terms?

A: Cubic trinomial 

You are encouraged to simplify radicals using mental math when possible. Moving forward, the step of simplifying radical expressions by writing them as expressions with fractional exponents will not be shown.