How do you simplify $3 \sqrt{15} \cdot 5 \sqrt{35}$ $3sqrt15 * 5sqrt35$ ?

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Answer 1 · 2018-05-18T00:48:47

See a solution process below:

First, rewrite the expression as:

$3 \cdot 5 \cdot \sqrt{15} \cdot \sqrt{35} \Rightarrow$ $3 * 5 * sqrt(15) * sqrt(35) =>$

$15 \cdot \sqrt{15} \cdot \sqrt{35}$ $15 * sqrt(15) * sqrt(35)$

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

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

$15 \cdot \sqrt{15} \cdot \sqrt{35} \Rightarrow$ $15 * sqrt(color(red)(15)) * sqrt(color(blue)(35)) =>$

$15 \cdot \sqrt{15 \cdot 35} \Rightarrow$ $15 * sqrt(color(red)(15) * color(blue)(35)) =>$

$15 \cdot \sqrt{525}$ $15 * sqrt(525)$

Then, rewrite the term under the radical as:

$15 \cdot \sqrt{25 \cdot 21} \Rightarrow$ $15 * sqrt(color(red)(25) * color(blue)(21)) =>$

$15 \cdot \sqrt{25} \cdot \sqrt{21} \Rightarrow$ $15 * sqrt(color(red)(25)) * sqrt(color(blue)(21)) =>$

$15 \cdot 5 \cdot \sqrt{21} \Rightarrow$ $15 * 5 * sqrt(color(blue)(21)) =>$

$75 \sqrt{21}$ $75sqrt(21)$

How do you simplify 3sqrt15 * 5sqrt353√15⋅5√353sqrt15 * 5sqrt35?