Question

Simplify the radical expression by rationalizing the denominator.

Answer 1

\[\frac{ 4 }{ \sqrt{11} }\]

Answer 2

do you know what "rationalizing the denominator" means?

Answer 3

isnt the square root of 11 irrational? so wouldnt it be no solution

Answer 4

\(\sqrt{11}\) is indeed irrational. so "rationalizing the denominator" means - change the denominator into a "rational number"

Answer 5

i think it means converting a irrational number into a rational number

Answer 6

yes - exactly

Answer 7

now, do you agree that if you multiply any number by one, then the number remains the same?

Answer 8

yeah

Answer 9

good - ow the "trick" to spot here is that you can write one as:\[1=\frac{\sqrt{11}}{\sqrt{11}}\]

Answer 10

so, if you multiply \(\frac{4}{\sqrt{11}}\) by \(\frac{\sqrt{11}}{\sqrt{11}}\) the value of the resulting number should not change

Answer 11

agreed?

Answer 12

yes

Answer 13

*I meant "now the ..." up there

Answer 14

\[4 \sqrt{11}\]

im guessing that, that is my answer ^^

Answer 15

not quite - so we can then do:\[\frac{4}{\sqrt{11}}=\frac{4}{\sqrt{11}}\times\frac{\sqrt{11}}{\sqrt{11}}=\frac{4\sqrt{11}}{11}\]

Answer 16

we have now rationalized the denominator

Answer 17

hope that makes sense

Answer 18

oh my that makes so much sense. Thanks!! :)


would you like to help me with another question?

Answer 19

sure - but please post it as a new question

Answer 20

okay :)

Answer 21

thx :)