How do you simplify #sqrt (15x) * (21x)#?

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Answer 1 · 2015-05-18T14:38:16

By exponentiial rules, we know that #a^n*a^m=a^(n+m)#

So, in this case, if we rewrite your product:

#(15x)^(1/2)*(21x)=15^(1/2)*x^(1/2)*21x#

We can sum the exponentials of the variable #x#.

#15^(1/2)*21x^(3/2)#

Simpifying more, we can even factor the constants, as both are multplied by three:

#5^(1/2)*color(green)(3(1/2))*7*color(green)(3)*x^(3/2)#

#5^(1/2)*7*3^(3/2)*x^(3/2)#

Transforming all these exponentials into roots:

#7sqrt(5)sqrt((3x)^3)#