How do you simplify $3sqrt15 * 5sqrt35$ ?

Question

1644 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-05-18T00:48:47

See a solution process below:

First, rewrite the expression as:

$3 * 5 * sqrt(15) * sqrt(35) =>$

$15 * sqrt(15) * sqrt(35)$

Next, use this rule for radicals to simplify the radicals:

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

$15 * sqrt(color(red)(15)) * sqrt(color(blue)(35)) =>$

$15 * sqrt(color(red)(15) * color(blue)(35)) =>$

$15 * sqrt(525)$

Then, rewrite the term under the radical as:

$15 * sqrt(color(red)(25) * color(blue)(21)) =>$

$15 * sqrt(color(red)(25)) * sqrt(color(blue)(21)) =>$

$15 * 5 * sqrt(color(blue)(21)) =>$

$75sqrt(21)$

How do you simplify 3sqrt15 * 5sqrt353sqrt15 * 5sqrt35?