Divide Binomials by Monomials (Values and Variables) (Level 3)

This math topic focuses on dividing binomials by monomials involving both numerical values and variables under radical expressions at Level 3 complexity. It is part of an introductory series on radical divisions. The problems require simplifying complex radical expressions formed through division to get to the simplest form. Each question presents a radical expression where students need to perform division and then simplify, offering multiple choice answers for selection. This practice helps enhance skills in manipulating radicals and understanding algebraic operations involving square roots and powers with variables.

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
Math worksheet on 'Radicals - Divide Binomials by 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{5pxsquare root of 13px + psquare root of 5}{pxsquare root of 2px}
a A LaTex expression showing \frac{2p{x} to the power of 2 square root of 26 + square root of 10px}{2px}
b A LaTex expression showing \frac{5p{x} to the power of 2 square root of 26 + square root of 10px}{2p{x} to the power of 2 }
c A LaTex expression showing \frac{5p{x} to the power of 2 square root of 26 + 4square root of 10px}{2p{x} to the power of 2 }
d A LaTex expression showing \frac{5p{x} to the power of 2 square root of 26 + square root of 10px}{2{x} to the power of 2 }
e A LaTex expression showing \frac{5p{x} to the power of 2 square root of 26 - square root of 10px}{2p{x} to the power of 3 }
2
Divide the radical expressions and simplify the answer
A LaTex expression showing \frac{ysquare root of 11yr + 5square root of 2}{{y} to the power of 2 square root of 5}
a A LaTex expression showing \frac{ysquare root of 55yr + 5square root of 10}{5{y} to the power of 2 }
b A LaTex expression showing \frac{ysquare root of 55yr + 5square root of 10}{{y} to the power of 2 }
c A LaTex expression showing \frac{yrsquare root of 55yr + 5square root of 10}{4{y} to the power of 2 }
d A LaTex expression showing \frac{ysquare root of 55yr + square root of 10}{{y} to the power of 2 }
3
Divide the radical expressions and simplify the answer
A LaTex expression showing \frac{rsquare root of 5y + 3square root of 3y}{rsquare root of 3ry}
a A LaTex expression showing \frac{4rsquare root of 15r + 9square root of r}{3{r} to the power of 4 }
b A LaTex expression showing \frac{rsquare root of 15 + 9square root of r}{3{r} to the power of 2 {y} to the power of -1 }
c A LaTex expression showing \frac{{r} to the power of 2 square root of 30 - 9square root of 2r}{6{r} to the power of 2 }
d A LaTex expression showing \frac{rsquare root of 15{r to the power of -1 } + 9square root of r}{3{r} to the power of 2 y}
e A LaTex expression showing \frac{rsquare root of 15r + 9square root of r}{3{r} to the power of 2 }
4
Divide the radical expressions and simplify the answer
A LaTex expression showing \frac{csquare root of 2 - 3czsquare root of 3cz}{{c} to the power of 2 {z} to the power of 2 square root of 5}
a A LaTex expression showing \frac{2 - 3zsquare root of 15cz}{2c{z} to the power of 2 }
b A LaTex expression showing \frac{square root of 10 - zsquare root of 15cz}{5{z} to the power of 2 }
c A LaTex expression showing \frac{square root of 10 + 3czsquare root of 15z}{5c}
d A LaTex expression showing \frac{3square root of 10 - 3zsquare root of 15cz}{c{z} to the power of 2 }
e A LaTex expression showing \frac{square root of 10 - 3zsquare root of 15cz}{5c{z} to the power of 2 }
5
Divide the radical expressions and simplify the answer
A LaTex expression showing \frac{3dsquare root of 13 - d{x} to the power of 2 square root of 3}{dsquare root of 11dx}
a A LaTex expression showing \frac{3square root of 143dx + {x} to the power of 2 square root of 33{d to the power of -1 x}}{11d{x} to the power of 3 }
b A LaTex expression showing \frac{3dsquare root of 143x - {x} to the power of 2 square root of 33dx}{4dx}
c A LaTex expression showing \frac{3square root of 143dx - {x} to the power of 2 square root of 33dx}{11dx}
d A LaTex expression showing \frac{3square root of 143dx + d{x} to the power of 2 square root of 33dx}{11d{x} to the power of -1 }
e A LaTex expression showing \frac{3square root of 143dx + 2{x} to the power of 2 square root of 33dx}{11{d} to the power of -1 x}
6
Divide the radical expressions and simplify the answer
A LaTex expression showing \frac{c{p} to the power of 2 square root of 3c + 2{c} to the power of 2 psquare root of 5}{psquare root of 2cp}
a A LaTex expression showing \frac{pcsquare root of 6{p to the power of -1 } + 2csquare root of 10cp}{p}
b A LaTex expression showing \frac{pcsquare root of 6p + 2csquare root of 10cp}{2p}
c A LaTex expression showing \frac{p{c} to the power of -1 square root of 6p + 2csquare root of 10cp}{p}
d A LaTex expression showing \frac{pcsquare root of 6p + 2csquare root of cp}{2p{c} to the power of -2 }
e A LaTex expression showing \frac{csquare root of 6p + 2csquare root of 10cp}{2p}
7
Divide the radical expressions and simplify the answer
A LaTex expression showing \frac{{b} to the power of 2 square root of 13 + 2dsquare root of 5b}{square root of 7}
a A LaTex expression showing {b} to the power of 2 square root of 91 - 2dsquare root of 35{b to the power of -1 }
b A LaTex expression showing \frac{{b} to the power of 2 square root of 91 + 2square root of 35b}{7}
c A LaTex expression showing \frac{{b} to the power of 2 square root of 91 + 2dsquare root of 35b}{7}
d A LaTex expression showing {b} to the power of 2 square root of 91 + 2dsquare root of 35{b to the power of -1 }
e A LaTex expression showing {b} to the power of 2 - 2dsquare root of 35b