How do you rationalize 10/sqrt810√8?

1 Answer
smendyka
May 18, 2018

See a solution process below:

Explanation:

To rationalize a fraction you need to multiply the fraction by the appropriate form of 11 to eliminate the radical in the denominator:

sqrt(8)/sqrt(8) * 10/sqrt(8) => (sqrt(8) * 10) /(sqrt(8) * sqrt(8)) => (10sqrt(8))/8√8√8⋅10√8⇒√8⋅10√8⋅√8⇒10√88

We can simplify this expression as:

(10sqrt(8))/8 => (10sqrt(4 * 2))/8 => (10sqrt(4)sqrt(2))/8 => (10 * 2sqrt(2))/8 => (20sqrt(2))/8 =>10√88⇒10√4⋅28⇒10√4√28⇒10⋅2√28⇒20√28⇒

(4 * 5sqrt(2))/(4 * 2) => (color(red)(cancel(color(black)(4))) * 5sqrt(2))/(color(red)(cancel(color(black)(4))) * 2) => (5sqrt(2))/2

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