Question

How do you simplify `\sqrt { 2} \sqrt { 74}`?

Answer 1

See a solution process below:

Explanation:

We can use these two rules for radicals to simplify this expression:

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

`sqrt(color(red)(2))sqrt(color(blue)(74)) => sqrt(color(red)(2) * color(blue)(74)) => sqrt(148)`

`sqrt(148) => sqrt(color(red)(4) * color(blue)(37)) => sqrt(color(red)(4))sqrt(color(blue)(37)) => 2sqrt(37)`