Ray's New Practical Arithmetic · Arts. 244–245 · Unit 24: Involution and Evolution
114. Cube root practice; the side of a cube
Goal: Your child extracts cube roots of whole numbers, decimals and fractions, and finds the side of a cube from its volume.
You'll need
- Paper and pencil, or a slate or small whiteboard
What's in the book
Page 313 works ∛413.5147 = 7.45+. Page 314 shows fractions and gives the full six-step rule. Page 315 has the practice list and Art. 245 (side of a cube) with problems. Answers are printed.
The lesson, step by step
Warm-up
Ask your child to tell you the steps of yesterday's cube root in their own words.
The rule
3. Square the root found, and multiply it by 300 for a trial divisor.
4. Multiply the preceding figure, or figures, of the root by the last and by 30, and square the last figure; add the products to the trial divisor; the sum is the complete divisor.
5. Multiply the complete divisor by the last figure of the root; subtract the product from the dividend, and to the remainder bring down the next period for a new dividend.
Decimals and fractions
Extract the cube root of 413.5147.
Point off 413.514|700 and work: 7.45+.
For a fraction whose terms are perfect cubes, take each root: ∛(2197/13824) = 13/24. Otherwise change it to a decimal first: ∛(4/5) = ∛.8 = .928+.
Side of a cube
Extract the cube root of the solid contents.
The contents of a cubical cellar are 1953.125 cu. ft.: find the length of one side.
Guided practice
Do these together:
A cubical box contains 512 half-inch cubes: what are the dimensions of the box inside?
Find the side of a cube equal to a mass 288 ft. long, 216 ft. broad, and 48 ft. high.
Independent practice and check
Your child works four or five from the list on page 315 and the rest of the Art. 245 problems. The book prints the answer at the end of each problem line. Have your child cover the answers with a strip of paper, work the problem, then slide the strip down to check.