How do you simplify #1/sqrt7#?
All you can do is rationalize the denominator.
To rationalize the denominator just means to make the denominator a rational number. We can do this by multiplying the numerator and the denominator by
This is as far as we can simplify. Here are the two rules about rationalizing a denominator:
When a monomial (one term in the denominator): Multiply the numerator and the denominator by the radical in the original expression's denominator
When a binomial (two terms in the denominator): Multiply the numerator and the denominator by the conjugate of the radical in the original expression. The conjugate forms a difference of squares. Example:
- Simplify completely. Don't forget: you can only multiply non radicals with non radicals and radicals with radicals. Example:
#3 xx sqrt(7) = 3sqrt(7)#while #sqrt(3) xx sqrt(7) = sqrt(21)#
2. Challenge question:
Rationalise the denominator of