Question

How do you rationalize the denominator and simplify `sqrt(10/7)`?

Answer 1

`sqrt(70)/7`

Explanation:

`sqrt(10/7)=sqrt(10)/sqrt(7)`

To rationalise this denominatir, we multiply the top and bottom by `sqrt(7)`, so we get `sqrt(10)/sqrt(7)*sqrt(7)/sqrt(7)`, `sqrt(7)*sqrt(7)` is just `7`, and `sqrt(10)*sqrt(7)=sqrt(10*7)=sqrt(70)`, as `70` doesn't have any factors which are perfect squares, it can only stay as `sqrt(70)`, giving us `sqrt(70)/7`

Answer 2

See the solution process below:

Explanation:

First, we need to rewrite the expression using this rule for dividing radicals:

`sqrt(color(red)(a)/color(blue)(b)) = sqrt(color(red)(a))/sqrt(color(blue)(b))`

`sqrt(color(red)(10)/color(blue)(7)) = sqrt(color(red)(10))/sqrt(color(blue)(7))`

Next, we can rationalize the denominator and remove the radical by multiplying the fraction by the appropriate form of `1`:

`sqrt(7)/sqrt(7) xx sqrt(10)/sqrt(7) = (sqrt(7) xx sqrt(10))/(sqrt(7) xx sqrt(7)) = (sqrt(7) xx sqrt(10))/7`

We can now use this rule of exponents to simplify the numerator:

`sqrt(color(red)(a)) * sqrt(color(blue)(b)) = sqrt(color(red)(a) * color(blue)(b))`

`(sqrt(color(red)(7)) * sqrt(color(blue)(10)))/7 = sqrt(color(red)(7) * color(blue)(10))/7 = sqrt(70)/7`