What is the square root of 32 over square root of 8?

1 Answer
Mar 21, 2018

See a solution process below:

Explanation:

We can rewrite this expression as:

sqrt(32)/sqrt(8) => sqrt(8 * 4)/sqrt(8)

Now, we can use this rule for radicals to rewrite the numerator and complete the simplification:

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

sqrt(color(red)(8) * color(blue)(4))/sqrt(8) =>

(sqrt(color(red)(8)) * sqrt(color(blue)(4)))/sqrt(8) =>

(cancel(sqrt(color(red)(8))) * sqrt(color(blue)(4)))/color(red)(cancel(color(black)(sqrt(8)))) =>

sqrt(color(blue)(4)) =>

2

We can also use this rule of radicals to rewrite and simplify the expression:

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

sqrt(color(red)(32))/sqrt(color(blue)(8)) =>

sqrt(color(red)(32)/color(blue)(8)) =>

sqrt(4) =>

2