Question

Question #f1fbe

Answer 1

`(5sqrt(2))/2`

Explanation:

`sqrt(8)=sqrt(4times2)=sqrt(4) times sqrt(2)=2sqrt(2)`

`cancel(10)/(cancel(2)sqrt(2))=5/sqrt(2)` simplifying top and bottom

`5/sqrt(2) times sqrt(2)/sqrt(2)` rationalising the denominator

`(5sqrt(2))/2`

Answer 2

See a solution process below:

Explanation:

We can rewrite this as:

`10/sqrt(8)`

We can also rewrite the square root of 8 as:

`10/sqrt(4 * 2)`

Using this rule we can simplify the denominator to:

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

`10/sqrt(color(red)(4) * color(blue)(2)) => 10/(sqrt(color(red)(4))sqrt(color(blue)(2))) => 10/(2sqrt(2)) => 5/sqrt(2)`

If necessary, we can rationalize the denominator or, in other words, eliminate all radicals from the denominator, by multiplying the fraction by the appropriate form of `1`:

`5/sqrt(2) * sqrt(2)/sqrt(2) => (5 * sqrt(2))/(sqrt(2) * sqrt(2)) => (5sqrt(2))/2`

Also, if necessary we can convert this to a single number as:

`(5sqrt(2))/2 => (5 * 1.4142)/2 => 7.0710/2` => 3.536#

Rounded to the nearest thousandth.