# CUBE ROOTS Write down some statements about the CUBE ROOTS Write down some statements about the shape you see. Be specific as possible. Perfect Cubes and Cube Roots A number is a perfect cube if you can take that many 1 x 1 x 1 unit cubes and form them into a cube. So how many perfect cubes could you make given 1000 blocks that are 1 x 1 x 1? Perfect Cubes and Cube Roots Side Volume Volume Length Operation Perfect Cube

1 unit 1x1x1 1 units 1 2 units 2x2x2 2 units 8 Perfect Cubes and Cube Roots Side Volume Volume Length Operation Perfect Cube

1 unit 13 1 units3 1 2 units 23 8 units3 8 3 units 33 27 units3 27

Perfect Cubes and Cube Roots Side Volume Volume Length Operation Perfect Cube 1 unit 13 1 units3 1 2 units 23 8 units3

8 3 units 33 27 units3 27 4 units Perfect Cubes and Cube Roots Side Volume Volume Length Operation Perfect Cube 1 unit 13

1 units3 1 2 units 23 8 units3 8 3 units 33 27 units3 27 4 units 43

Perfect Cubes and Cube Roots Side Volume Volume Length Operation Perfect Cube 1 unit 13 1 units3 1 2 units 23 8 units3

8 3 units 33 27 units3 27 4 units 43 64 units3 Perfect Cubes and Cube Roots Side Volume Volume Length Operation Perfect Cube

1 unit 13 1 units3 1 2 units 23 8 units3 8 3 units 33 27 units3 27

4 units 43 64 units3 64 Perfect Cubes and Cube Roots Side Volume Length Operation of cube Volume of cube Perfect Cube 1 unit 13

1 units3 1 2 units 23 8 units3 8 3 units 33 27 units3 27 4 units 43

64 units3 64 x units x3 p units3 So, x= p Common Core #4 Evaluate perfect cube roots in the form of x = p and estimate non-perfect cube roots to the nearest tenth. Perfect Cubes and Cube Roots Square Root Cube Root

SAMPLE QUESTIONS Find the cube root of a given number, p. For example what is the cube root of 9,261? Answer is 21 because 21=9,261 Find the cube root for the following: (1)x = 2197 (2) b = 4913 (3) Answers are 13, 17, and 12 3 1728 SAMPLE HARDER QUESTIONS Estimate cube roots. For example, to the nearest tenth, what is the cube root of 3? We know 1 = 1 and 2 = 8 so the answer lies somewhere between 1 and 2. You must pick a number say 1.4 and multiply it three times and see how close it is to the number 3. 1.4 = 2.744 Close but we need to now check 1.5.. 1.5 = 3.375 So 1.4 is the best answer since it is closer to 3 than 1.5

YOU TRY THESE Estimate the cube root to the nearest tenth by finding x. (1) x = 11 (2) Answers are (1) 2.2 and (2) 4.6 And (3) 8.3 3 (3) x = 562 99