What is the equivalent radical expression for the exponential expression below? 18^1/2

Question

3745 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-07-25T21:32:29

See a solution process below:

Use this rule to change the term to a radical:

$x^(1/color(red)(n)) = root(color(red)(n))(x)$

$18^(1/color(red)(2)) => root(color(red)(2))(18) => sqrt(18)$

We can simplify this expression, if necessary, by using this rule for radicals:

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

$sqrt(18) => sqrt(color(red)(9) * color(blue)(2)) => sqrt(color(red)(9)) * sqrt(color(blue)(2)) => 3sqrt(2)$

Answer 2 · 2018-07-25T21:33:35

See below

$a^(m/n)= rootn(a^m)$

$18^(1/2)= sqrt18= sqrt(9*2)= 3sqrt2$