Pass Check: Surds
Simplify surds and rationalise denominators containing square roots.
Surd
An irrational root, such as √2 or √5, that cannot be simplified to a whole number or exact decimal.
Rationalise the denominator
Rewrite a fraction so there is no surd left in the denominator.
Simplest form (surd)
A surd written with the smallest possible number under the root sign, e.g. √50 = 5√2.
Conjugate
For a denominator a + √b, the conjugate is a − √b; multiplying by it removes the surd.
Quick check
Mixed quiz
1. Expand and simplify (sqrt(2) + sqrt(4))^2.
2. Simplify sqrt(32).
3. Expand and simplify (sqrt(3) + sqrt(3))^2.
4. Expand and simplify (sqrt(3) + sqrt(4))^2.
5. Simplify sqrt(180).
6. Expand and simplify (sqrt(2) + sqrt(3))^2.
7. Which of these is a surd?
8. Which expression is equivalent to (1+√2)²?