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

Question

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

2 Answers

Impact of this question

3743 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-07-25T21:32:29

See a solution process below:

Explanation:

Use this rule to change the term to a radical:

$x^{\frac{1}{n}} = \sqrt[n]{x}$ $x^(1/color(red)(n)) = root(color(red)(n))(x)$

$18^{\frac{1}{2}} \Rightarrow \sqrt[2]{18} \Rightarrow \sqrt{18}$ $18^(1/color(red)(2)) => root(color(red)(2))(18) => sqrt(18)$

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

$\sqrt{a \cdot b} = \sqrt{a} \cdot \sqrt{b}$ $sqrt(color(red)(a) * color(blue)(b)) = sqrt(color(red)(a)) * sqrt(color(blue)(b))$

$\sqrt{18} \Rightarrow \sqrt{9 \cdot 2} \Rightarrow \sqrt{9} \cdot \sqrt{2} \Rightarrow 3 \sqrt{2}$ $sqrt(18) => sqrt(color(red)(9) * color(blue)(2)) => sqrt(color(red)(9)) * sqrt(color(blue)(2)) => 3sqrt(2)$

Answer 2 · 2018-07-25T21:33:35

See below

Explanation:

$a^{\frac{m}{n}} = \sqrt[n]{a^{m}}$ $a^(m/n)= rootn(a^m)$

$18^{\frac{1}{2}} = \sqrt{18} = \sqrt{9 \cdot 2} = 3 \sqrt{2}$ $18^(1/2)= sqrt18= sqrt(9*2)= 3sqrt2$

Science

Math

Humanities

... and beyond

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

2 Answers

Explanation:

Explanation:

Related questions

Impact of this question