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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Math worksheet on 'Radicals - Divide Monomials (Values and Variables) (Level 3)'. Part of a broader unit on 'Radicals - Division Intro' Learn online: app.mobius.academy/math/units/radicals_division_intro/
1
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{square root of 21p}{7{p} to the power of -1 }
b A LaTex expression showing \frac{{n} to the power of 2 square root of 21p}{p}
c A LaTex expression showing \frac{p{n} to the power of 2 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{{n} to the power of 2 square root of 2p}{p}
2
Divide the radical expressions and simplify the answer
A LaTex expression showing \frac{square root of 28{m to the power of 3 {d} to the power of 2 }}{square root of 45m{d to the power of 2 }}
a A LaTex expression showing 2square root of 35
b A LaTex expression showing 2m
c A LaTex expression showing \frac{2msquare root of 35}{15}
d A LaTex expression showing msquare root of 35
3
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{square root of 35x}{5{m} to the power of 2 }
b A LaTex expression showing \frac{xsquare root of 35}{5{m} to the power of 2 {x} to the power of -1 }
c A LaTex expression showing \frac{xsquare root of 35}{5{m} to the power of 3 }
d A LaTex expression showing \frac{2square root of x}{5m}
e A LaTex expression showing \frac{4square root of 35x}{5{m} to the power of 2 {x} to the power of -1 }
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 275{y to the power of 3 {p} to the power of 2 }}{square root of 8{y to the power of 4 {p} to the power of 2 }}
a A LaTex expression showing \frac{5square root of 22y}{4{p} to the power of 2 }
b A LaTex expression showing \frac{5square root of 22{y to the power of -1 }}{4y}
c A LaTex expression showing \frac{5square root of y}{y}
d A LaTex expression showing \frac{5square root of 22y}{4y}
6
Divide the radical expressions and simplify the answer
A LaTex expression showing \frac{square root of 44z}{square root of 48{z to the power of 2 {b} to the power of 2 }}
a A LaTex expression showing \frac{square root of 33{z to the power of -1 }}{6b}
b A LaTex expression showing \frac{5square root of 33z}{6z{b} to the power of 2 }
c A LaTex expression showing \frac{square root of 33}{6z}
d A LaTex expression showing \frac{square root of 33}{6z{b} to the power of 3 }
e A LaTex expression showing \frac{square root of 33z}{6zb}
7
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{square root of 22z}{3z}
b A LaTex expression showing square root of 22
c A LaTex expression showing \frac{2square root of 22z}{z}
d A LaTex expression showing \frac{square root of 22}{3{z} to the power of -1 }
e A LaTex expression showing \frac{4square root of 22z}{3{z} to the power of 3 }