Divide Binomials by Monomials (Values and Variables) (Level 4)

This math topic focuses on dividing binomials by monomials, specifically working with radical expressions involving both numerical values and variables. It serves as an introductory exploration into the division of radicals, requiring the simplification of complex fractional expressions under the radical sign. Learners practice manipulating and simplifying these expressions with variable powers, coefficients, and different radicands across multiple-choice questions.

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

more
View

Radicals - Divide Binomials by Monomials (Values and Variables) Worksheet

Mobius Math Academy logo
Radicals - Divide Binomials by Monomials (Values and Variables)
1
Divide the radical expressions and simplify the answer
A LaTex expression showing \frac{4zmsquare root of 2m + {z} to the power of 2 {m} to the power of 2 square root of 2}{5{m} to the power of 2 square root of 5z}
a A LaTex expression showing \frac{4square root of 10zm + {m} to the power of 3 zsquare root of 10z}{25m}
b A LaTex expression showing 4square root of 10z + zsquare root of 10z
c A LaTex expression showing \frac{square root of 10zm - mzsquare root of 10z}{25mz}
d A LaTex expression showing \frac{4square root of 10zm + mzsquare root of 10z}{25m}
e A LaTex expression showing \frac{4square root of 10zm - m{z} to the power of 3 square root of 10z}{25{m} to the power of 2 }
2
Divide the radical expressions and simplify the answer
A LaTex expression showing \frac{5{p} to the power of 2 square root of 3 + {p} to the power of 2 {b} to the power of 2 square root of 11}{4pbsquare root of 3pb}
a A LaTex expression showing \frac{15square root of pb + bsquare root of 33pb}{{b} to the power of 2 }
b A LaTex expression showing \frac{15square root of pb + {b} to the power of 2 square root of 33pb}{12{p} to the power of -1 {b} to the power of 2 }
c A LaTex expression showing \frac{15square root of pb + {b} to the power of 2 square root of 33pb}{12{b} to the power of 2 }
d A LaTex expression showing \frac{15square root of pb + {b} to the power of 2 square root of 33pb}{{b} to the power of 2 }
3
Divide the radical expressions and simplify the answer
A LaTex expression showing \frac{mcsquare root of 2mc - 2csquare root of 11mc}{4m{c} to the power of 2 square root of 7m}
a A LaTex expression showing \frac{msquare root of 14c - 2square root of 77c}{28mc}
b A LaTex expression showing \frac{m{c} to the power of -1 square root of 14c + 2square root of 77c}{28{m} to the power of 3 c}
c A LaTex expression showing \frac{msquare root of 14c - 2csquare root of 77}{28m}
d A LaTex expression showing \frac{{m} to the power of 2 square root of 14c + 2square root of 77c}{mc}
e A LaTex expression showing \frac{msquare root of 14c + 3square root of 77c}{mc}
4
Divide the radical expressions and simplify the answer
A LaTex expression showing \frac{3ysquare root of 13y - {y} to the power of 2 square root of 13}{2ysquare root of 7m}
a A LaTex expression showing \frac{4square root of 91my + ysquare root of 91m}{m}
b A LaTex expression showing \frac{3square root of 91my - ysquare root of 91m}{14m}
c A LaTex expression showing \frac{3square root of 91my + ymsquare root of 91}{m}
d A LaTex expression showing \frac{3square root of 91my - ysquare root of 91{m to the power of -1 }}{m}
e A LaTex expression showing \frac{3square root of 91my + ysquare root of 91}{m}
5
Divide the radical expressions and simplify the answer
A LaTex expression showing \frac{3{c} to the power of 2 square root of 7r + rcsquare root of 2}{3square root of 2rc}
a A LaTex expression showing \frac{3csquare root of 42c - square root of 3rc}{18}
b A LaTex expression showing 3csquare root of 14c + 2square root of rc
c A LaTex expression showing \frac{3{c} to the power of -1 square root of 14c + 2square root of rc}{4}
d A LaTex expression showing \frac{3csquare root of 14 - 2square root of rc}{2}
e A LaTex expression showing \frac{3csquare root of 14c + 2square root of rc}{6}
6
Divide the radical expressions and simplify the answer
A LaTex expression showing \frac{3{r} to the power of 2 square root of 5b - rsquare root of 7b}{3{b} to the power of 2 {r} to the power of 2 square root of 2}
a A LaTex expression showing \frac{3rsquare root of 10b - square root of 14b}{6{b} to the power of 2 {r} to the power of 3 }
b A LaTex expression showing \frac{3rsquare root of 10 - square root of 14b}{{b} to the power of 2 r}
c A LaTex expression showing \frac{3rsquare root of 10b - square root of 14b}{6{b} to the power of 2 r}
d A LaTex expression showing \frac{3{r} to the power of 3 square root of 10b + square root of 14b}{6{b} to the power of 2 r}
e A LaTex expression showing \frac{3rsquare root of 10b - square root of 14b}{6{b} to the power of 4 r}
7
Divide the radical expressions and simplify the answer
A LaTex expression showing \frac{2rsquare root of 5 - p{r} to the power of 2 square root of 11}{4prsquare root of 13}
a A LaTex expression showing \frac{2square root of 65 - rsquare root of 143}{52pr}
b A LaTex expression showing \frac{2square root of 65 - pr}{52p}
c A LaTex expression showing \frac{2square root of 65 - prsquare root of 143}{52p}
d A LaTex expression showing \frac{4square root of 65 - prsquare root of 143}{p}
e A LaTex expression showing \frac{2square root of 65 - psquare root of 143}{p}
8
Divide the radical expressions and simplify the answer
A LaTex expression showing \frac{dzsquare root of 5d + 2square root of 5z}{4{d} to the power of 2 square root of 5z}
a A LaTex expression showing \frac{dsquare root of zd + 2}{4{d} to the power of 2 }
b A LaTex expression showing \frac{dsquare root of zd - 2}{2{d} to the power of 2 }
c A LaTex expression showing \frac{{d} to the power of 2 square root of zd + 2}{4{d} to the power of 2 }
d A LaTex expression showing \frac{{d} to the power of 2 square root of zd + 2}{{d} to the power of 2 }
e A LaTex expression showing \frac{dsquare root of zd + 2}{{d} to the power of 2 }