How do you simplify $3root4(24)*5root4(2)$ ?

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Answer 1 · 2017-06-11T14:49:11

See a solution process below:

First, rewrite this expression as:

$(3 * 5)(root(4)(24) * root(4)(2)) => 15(root(4)(24) * root(4)(2))$

Next use this rule for radicals to combine the radicals:

$root(n)(color(red)(a)) * root(n)(color(blue)(b)) = root(n)(color(red)(a) * color(blue)(b))$

$15(root(4)(color(red)(24)) * root(4)(color(blue)(2))) => 15root(4)(color(red)(24) * color(blue)(2)) => 5root(4)(48)$

Now, use this rule in reverse to complete the simplification:

$5root(4)(48) => 15root(4)(color(red)(16) * color(blue)(3)) => 15(root(4)(color(red)(16)) * root(4)(color(blue)(3))) => 15 * 2 * root(4)(3) =>$

$30root(4)(3)$

How do you simplify 3root4(24)*5root4(2)3root4(24)*5root4(2)?