Chapter 4 - Roots

Question 1

A square root has ONLY ONE value

Answer 1

x²= 16; x=4; x=-4 x = √16; x =4

If an EQUATION contains a **√, ONLY use the POSITIVE ROOT**

If an equation contains a SQUARED VARIABLE, and YOU TAKE the √, use both POSITIVE & NEGATIVE solutions

This rule applies to any EVEN ROOT and **ODD ROOTS. **

**ODD ROOTS **like ODD EXPONENTS, keep the sign of the base

Question 2

When can you simplify roots?

Answer 2

**REMEMBER: You can ONLY separate or combine the product or quotient of two roots. **

You cannot separate or combine the sum or difference of two roots.

Question 3

Simpify Roots

Answer 3

√25*16 = √25 * √16= 5 *4 = 20

√50 * √18= √50*18= √900= 30

√144/16 = √144 / √16 = 12/4 = 3

√72/√8 = √72/8 = √9 = 3

√16 + 9 = √16 + √9 = 4+3 = 7 INCORRECT

√16+9= √25= 5 CORRECT

Question 4

Simplifying roots of Imperfect Squares

Answer 4

√52= rewrite this as product of primes under the radical.

√52 = √2*2*13 = √2.2= √4= 2√13

Question 5

What is 216^1/3?

Answer 5

216^1/3

3√216 = Break out 216 into its prime factors

2. 2.2.3.3.3 = What # multiplied by itself 3 times will give 216.
3. 3=6; 2.3=6; 2.3= 6

So there are 3 pairs of 6 that will mulitply to 216

3√64 = Break out 64 into its prime factors

2. 2.2.2.2.2 = What # multiplied by itself 3 times will give 64
3. 2 =4; 2.2=4; 2.2=4 = There are 3 pairs of 4 that will make 64