# How do you simplify #1/sqrt7#?

##### 1 Answer

All you can do is rationalize the denominator.

#### Explanation:

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:

**Practice exercises:**

- 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)#

a)

b)

c)

d)

**2. Challenge question:**

Rationalise the denominator of