Powers and Roots

Getting back to our roots!

For this session we will need squares, cubes and their roots. Here is a reminder of how they work:

Reminders:

Squares and Square Roots:

3² = 9, so 3 = (9)^1/2 = ÷9

Cubes and Cube Roots:

3³ = 27, so 3 = (27)^1/3 = ³÷27

Fractional Powers:

(2)^3/2 = (2³)^1/2 = ÷8 = 2.8

Check: does this makes sense?
2² = 4 and 3²= 9, so ÷8 must be somewhere between 2 and 3.

(4)^2/3 = (4²)^1/3 = ³÷16 = 2.5

Check: does this makes sense?
2³= 8 and 3³= 27, so ³÷16 must be somewhere between 2 and 3.

Now it is your turn - try these:

(A) What is (5)^2/3? (a) 1.2, (b) 2.9, (c) 3.9, or (d) 17.1?

(B) What is (3)^3/2? (a) 1.2, (b) 2.1, (c) 5.2, or (d) 729?

	*Reminders:*
	Squares and Square Roots: 3² = 9, so 3 = (9)^1/2 = ÷9	Cubes and Cube Roots: 3³ = 27, so 3 = (27)^1/3 = ³÷27
	Fractional Powers:
	(2)^3/2 = (2³)^1/2 = ÷8 = 2.8 Check: does this makes sense? 2² = 4 and 3²= 9, so ÷8 must be somewhere between 2 and 3.	(4)^2/3 = (4²)^1/3 = ³÷16 = 2.5 Check: does this makes sense? 2³= 8 and 3³= 27, so ³÷16 must be somewhere between 2 and 3.