Ray's New Higher Arithmetic · Arts. 383–384 · Unit 26: Evolution
114. Horner's method optional
Goal: Your student follows Horner's column method to extract a root of any degree.
You'll need
- The book
- A slate, small whiteboard or scrap paper
- A notebook and pencil
- A calculator, for checking only (optional)
What's in the book
Horner's method: a rule for extracting any root by columns, a worked fourth root (68719476736), a contracted method, a cube root of 44.6 to six decimals, and examples (most answers printed).
The lesson, step by step
Introduce it
Read:
Horner's Method, named from its inventor, Mr. W. G. Horner, of Bath, England, may be advantageously applied in extracting any root, especially if the degree of the root be not a composite number.
Say"Not composite" means 5th or 7th roots, which can't be done by square and cube roots in turn.
The setup
Read the first rule:
Make as many columns as there are units in the index of the root to be extracted; place the given number at the head of the right-hand column, and ciphers at the head of the others.
Follow the book's example
Walk through the fourth root of 68719476736 in the book, column by column. Have your student copy each column. The root is 512 (check: 512⁴ = 68719476736).
Guided practice
Do a familiar one by Horner's method:
Extract the square root of 15625.
Then the cube root of 68719476736 (the same number as before).
Independent practice
Your student tries the fifth root example:
Extract the fifth root of 14348907.
A calculator may be used to check the last step only.
Wrap-up
Ask: Which method is easier for a square root, the one from Lesson 1044 or Horner's? Which would you use for a 5th root?
Tip
Horner's method is beyond what most students need. Skip it, or do it only with a student who loves arithmetic.
Answers to the book's problems
Fifth root of 14348907: 27 (27⁵ = 14348907).
Worked out for this site from the scan. If a number in your copy differs, trust the book.