Surds

What this chapter teaches

A surd is an exact root that is not a whole number, such as √2. To simplify one, take out the square root of the largest square factor, so √50 = 5√2. Like surds add as like things do, products multiply under one root, and a surd on the bottom of a fraction is removed by multiplying the top and bottom by it.

Three questions to ask

There is no one right wording. Listen for the idea.

1. What is the largest square factor of 50, and why does only 5 come out of the root?
2. Why can you add 2√2 and 3√2, but not √2 and √3?
3. How does multiplying top and bottom by √3 remove the root from 6/√3 without changing its value?

After the chapter, the learner can

• Simplify √50 to 5√2
• Add and multiply surds, like √8 + 3√2
• Rationalise the denominator of 6/√3