Divide Monomials (Values and Variables) (Level 3)

This math topic focuses on the skill of dividing monomial radical expressions and simplifying the results. It involves various algebraic operations where students manipulate expressions containing both radicals and variables. The problems require understanding how to handle square roots, powers, and coefficients within a division framework. The material is part of a broader introductory unit on the division of radicals. Each question provides multiple answer choices, suggesting a format that checks for understanding through problem solving and simplification of radical terms.

Work on practice problems directly here, or download the printable pdf worksheet to practice offline.

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Radicals - Divide Monomials (Values and Variables) Worksheet

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Radicals - Divide Monomials (Values and Variables)
1
Divide the radical expressions and simplify the answer
A LaTex expression showing \frac{square root of 117y{p to the power of 4 }}{square root of 12{y to the power of 2 {p} to the power of 2 }}
a A LaTex expression showing \frac{2psquare root of 39y}{{y} to the power of 2 }
b A LaTex expression showing \frac{psquare root of 39y}{2y}
c A LaTex expression showing \frac{psquare root of 39}{y}
d A LaTex expression showing \frac{{y} to the power of -1 psquare root of 39y}{y}
e A LaTex expression showing \frac{psquare root of 39{y to the power of -1 }}{4y}
2
Divide the radical expressions and simplify the answer
A LaTex expression showing \frac{square root of 12{p to the power of 3 {n} to the power of 4 }}{square root of 28{p to the power of 4 }}
a A LaTex expression showing \frac{{n} to the power of 2 square root of 2p}{p}
b A LaTex expression showing \frac{{n} to the power of 2 square root of 21p}{p}
c A LaTex expression showing \frac{square root of 21p}{7{p} to the power of -1 }
d A LaTex expression showing \frac{{n} to the power of 2 square root of 21p}{7p}
e A LaTex expression showing \frac{p{n} to the power of 2 square root of 21p}{7{p} to the power of -1 }
3
Divide the radical expressions and simplify the answer
A LaTex expression showing \frac{square root of 28{z to the power of 4 d}}{square root of 117{z to the power of 3 {d} to the power of 4 }}
a A LaTex expression showing \frac{2zsquare root of 91zd}{39{d} to the power of 4 }
b A LaTex expression showing \frac{square root of 91zd}{39}
c A LaTex expression showing \frac{2square root of 91z}{{d} to the power of 2 }
d A LaTex expression showing \frac{2square root of 91d}{{d} to the power of 2 }
e A LaTex expression showing \frac{2square root of 91zd}{39{d} to the power of 2 }
4
Divide the radical expressions and simplify the answer
A LaTex expression showing \frac{square root of 8{p to the power of 3 {x} to the power of 2 }}{square root of 275{p to the power of 3 {x} to the power of 4 }}
a A LaTex expression showing \frac{square root of 22}{55{x} to the power of 2 }
b A LaTex expression showing \frac{2square root of 22}{55x}
c A LaTex expression showing \frac{square root of 22}{55{p} to the power of -2 x}
d A LaTex expression showing \frac{3square root of 22}{x}
e A LaTex expression showing \frac{square root of 22}{55{x} to the power of 3 }
5
Divide the radical expressions and simplify the answer
A LaTex expression showing \frac{square root of 99x}{square root of 48nx}
a A LaTex expression showing \frac{square root of 33n}{4n}
b A LaTex expression showing \frac{square root of 33n}{n{x} to the power of -2 }
c A LaTex expression showing \frac{square root of n}{4{n} to the power of 2 }
d A LaTex expression showing \frac{square root of 33}{4}
6
Divide the radical expressions and simplify the answer
A LaTex expression showing \frac{square root of 32r{d to the power of 3 }}{square root of 80{r to the power of 4 d}}
a A LaTex expression showing \frac{dsquare root of 10}{5r}
b A LaTex expression showing \frac{square root of 10r}{5{r} to the power of 4 }
c A LaTex expression showing \frac{dsquare root of 10r}{5{r} to the power of 3 }
d A LaTex expression showing \frac{dsquare root of 10{r to the power of -1 }}{5{r} to the power of 3 }
e A LaTex expression showing \frac{dsquare root of 10r}{5{r} to the power of 2 }
7
Divide the radical expressions and simplify the answer
A LaTex expression showing \frac{square root of 63{x to the power of 3 }}{square root of 45{m to the power of 4 {x} to the power of 2 }}
a A LaTex expression showing \frac{xsquare root of 35}{5{m} to the power of 2 {x} to the power of -1 }
b A LaTex expression showing \frac{2square root of x}{5m}
c A LaTex expression showing \frac{xsquare root of 35}{5{m} to the power of 3 }
d A LaTex expression showing \frac{square root of 35x}{5{m} to the power of 2 }
e A LaTex expression showing \frac{4square root of 35x}{5{m} to the power of 2 {x} to the power of -1 }
8
Divide the radical expressions and simplify the answer
A LaTex expression showing \frac{square root of 44{r to the power of 2 z}}{square root of 18{r to the power of 2 {z} to the power of 2 }}
a A LaTex expression showing \frac{2square root of 22z}{z}
b A LaTex expression showing \frac{square root of 22z}{3z}
c A LaTex expression showing \frac{4square root of 22z}{3{z} to the power of 3 }
d A LaTex expression showing square root of 22
e A LaTex expression showing \frac{square root of 22}{3{z} to the power of -1 }