Ray's New Practical Arithmetic · Art. 238 · Unit 24: Involution and Evolution
111. Extracting the square root
Goal: Your child extracts the square root of a whole number or decimal by the long method, and understands it with the square-and-strips picture.
You'll need
- Paper and pencil, or a slate or small whiteboard
- Grid paper (optional, for the square-and-strips picture)
What's in the book
Page 303 begins Art. 238 with the worked example √256. Page 304 gives the geometrical explanation with a diagram. Page 305 works decimals and fractions and gives the rule, finished on page 306 with many problems. Answers are printed.
The lesson, step by step
Warm-up
Ask: 16 × 16 = ? (256.) We are going to work backward from 256 to 16.
Work the book's example
Extract the square root of 256.
Point off: 2|56. The largest square in 2 is 1; write 1 in the root and subtract, leaving 1. Bring down 56: 156.
Double the root (2) for a trial divisor. 2 goes into 15 about 6 times, so write 6 in the root and after the 2, making 26. 26 × 6 = 156, remainder 0. The root is 16.
The picture
Draw the diagram from page 304: a 10 × 10 square (100), two strips 10 × 6 (60 each), and a small 6 × 6 square (36). Total 256.
The "double the root" step is the two strips. The digit written on the end is the small corner square.
Hence, the square root of 256 is 16; or, when 256 sq. in. are arranged in the form of a square, each side is 16 inches.
Decimals and fractions
Extract the square root of 758.436.
Point off from the decimal point both ways (7|58.43|60) and work as before: 27.53+.
By bringing down one or more periods of decimal ciphers, the operation might be continued to any required number of decimal places in the root.
For a fraction like 256/625, take the root of each term: 16/25.
Guided practice
Work two from the list on page 306 together: 529 and 234.09.
Independent practice and check
Your child works about eight more from page 306. 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.