Question

Use Property 1 for radicals to simplify the following radical expression as much as possible. Assume the variable represents a positive number.

Answer 1

\[\frac{ 3 }{ 2 }\sqrt{24x^3}\]

Answer 2

can you factor 24 ?

Answer 3

4 & 6

Answer 4

and \(x^3 = x \times x^2\)


so,
\(\Large \sqrt {24x^3 } = \sqrt 4 \sqrt 6 \sqrt x \sqrt {x^2} \)

Answer 5

simplify 1st and last term

Answer 6

2 & x

Answer 7

\(\Large \sqrt {24x^3 } = \sqrt 4 \sqrt 6 \sqrt x \sqrt {x^2} = 2x \sqrt {6x}\)
thats it!
cannot be further simplified.

Answer 8

Yaaay! Thanks!

Answer 9

don't forget the initial 3/2

Answer 10

so final answer will be
\(3x \sqrt {6x}\)