Ray's New Elementary Algebra · Arts. 200–203 · Unit 6: Chapter VI: Powers, roots and radicals
43. Adding, subtracting, multiplying and dividing radicals
Goal: Your student does all four operations with radicals of the second degree.
You'll need
- The book, open to the page
- Pencil and plenty of paper (or a whiteboard)
- A card to cover printed answers
What's in the book
Addition and subtraction of radicals (combine similar ones after reducing), multiplication (multiply coefficients and quantities under the sign), and division, each with its rule and exercises. Answers are printed.
The lesson, step by step
Warm-up
Simplify √8, √18 and √50. (2√2, 3√2, 5√2.)
Adding and subtracting
Read Arts. 200 and 201.
2. If the radicals are similar, add the coefficients, and annex the common radical.
Work example 3: √8 + √18 = 2√2 + 3√2 = 5√2.
Guided practice
5. √20 and √80 Ans. 6√5.
Then subtraction example 2: √32 − √8 = 4√2 − 2√2 = 2√2.
Multiplying
Read Art. 202.
Multiply the coefficients together for a new coefficient, and the quantities under the radical sign for a new radical.
Work example 2: 2√14 × 3√2 = 6√28 = 12√7. Then exercise 11, (2 + √2)(2 − √2) = 4 − 2 = 2.
Dividing
Read Art. 203.
Divide the coefficient of the dividend by the coefficient of the divisor for a new coefficient, and the radical of the dividend by the radical of the divisor for a new radical.
Example 1: 8√72 ÷ 2√6 = 4√12 = 8√3.
Independent practice
A selection from each article: addition 4, 6, 7; subtraction 3 to 7; multiplication 3 to 8 and 15 to 17; division 2 to 6.
Wrap-up
Ask: Why can't 2√3 + 5√7 be combined into one term?
Tip
Always reduce first. Many radicals that look different turn out to be similar.
Answers to the book's problems
The book prints the answer after each exercise.
Worked out for this site from the scan. If a number in your copy differs, trust the book. Every answer is in the Key ↗.