How do you simplify #1/sqrt7#?

1 Answer
Feb 19, 2016

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 #sqrt(7)#, in order to keep the expression equivalent.

#1/sqrt(7) xx sqrt(7)/sqrt(7)#

#= sqrt(7)/sqrt(49)#

#= sqrt(7)/7#

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: #sqrt(2) + 4# is the conjugate of #sqrt(2) - 4#. Essentially, you must switch the sign in the middle.

Practice exercises:

  1. 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) #4/sqrt(5)#

b) #(3 + sqrt(6))/sqrt(2)#

c) #(5 - sqrt(7))/(sqrt(10) - sqrt(11))#

d) #(sqrt(3) + sqrt(2))/(5 + sqrt(6))#

2. Challenge question:

Rationalise the denominator of #sqrt(2)/sqrt((x^2 + 6x + 5))#