How do you multiply #\sqrt { m ^ { 25} n ^ { 20} } \cdot \sqrt { m ^ { 7} n ^ { 3} }#?

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Answer 1 · 2017-07-21T21:55:30

See a solution process below:

First, use this rule for radicals to rewrite the expression:

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

#sqrt(m^25n^20) * sqrt(m^7n^3) =>#

#sqrt(m^25n^20 * m^7n^3) =>#

#sqrt(m^25 * m^7 * n^20 * n^3) =>#

#sqrt(m^(25+7) * n^(20+3)) =>#

#sqrt(m^32n^23)#

If necessary, we can simplify this expression by rewriting the expression as:

#sqrt(m^32n^22 * n^1) =>#

#sqrt(m^32n^22 * n)#

We can then use this rule to complete the simplification:

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

#sqrt(m^32n^22 * n) =>#

#sqrt(m^32n^22) * sqrt(n) =>#

#m^16n^11sqrt(n)#