Radical

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.

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Divide Binomials by Monomials (Values and Variables)

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Divide the radical expressions and simplify the answer

27ny+ny3yy7n\frac{2\sqrt{7ny} + ny\sqrt{3y}}{y\sqrt{7n}}

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

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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{{b} to the power of 2 xsquare root of 7x + 3bxsquare root of 2b}{xsquare root of 2x}
a A LaTex expression showing \frac{2x{b} to the power of 2 square root of 14 + 6bsquare root of xb}{5x}
b A LaTex expression showing \frac{x{b} to the power of 2 square root of 14 - 6square root of xb}{2x}
c A LaTex expression showing \frac{x{b} to the power of 2 square root of 14 - 6{b} to the power of 2 square root of x}{3x}
d A LaTex expression showing {b} to the power of 2 square root of 14 - 6bsquare root of xb
e A LaTex expression showing \frac{{b} to the power of 2 square root of 14 + 6bsquare root of b}{2{x} to the power of 2 }
f A LaTex expression showing \frac{x{b} to the power of 2 square root of 14 + 6bsquare root of xb}{2x}
2
Divide the radical expressions and simplify the answer
A LaTex expression showing \frac{r{b} to the power of 2 square root of 3r + 5{r} to the power of 2 {b} to the power of 2 square root of 7}{bsquare root of 13b}
a A LaTex expression showing {r} to the power of 2 square root of 39br + 5{r} to the power of 2 square root of 91b
b A LaTex expression showing \frac{3rsquare root of 39br - 5{r} to the power of 2 square root of 91b}{13}
c A LaTex expression showing \frac{rsquare root of 39br + 5{r} to the power of 2 square root of 91b}{13}
d A LaTex expression showing rsquare root of 39b + 5{r} to the power of 2 square root of 91b
e A LaTex expression showing \frac{brsquare root of 39br + 5{r} to the power of 2 square root of 91b}{13}
f A LaTex expression showing rsquare root of 39br + 5{r} to the power of 2 square root of 91{b to the power of -1 }
3
Divide the radical expressions and simplify the answer
A LaTex expression showing \frac{5{b} to the power of 2 square root of 5 + square root of 5}{{b} to the power of 2 square root of 3c}
a A LaTex expression showing \frac{5{b} to the power of 2 square root of 15c + square root of c}{3{b} to the power of 4 c}
b A LaTex expression showing \frac{5bsquare root of 15c + square root of 15c}{3c}
c A LaTex expression showing \frac{5{b} to the power of 2 square root of 15c + square root of 15}{4{b} to the power of 2 c}
d A LaTex expression showing \frac{5{b} to the power of 2 square root of 15c + square root of 15c}{3{b} to the power of 2 c}
e A LaTex expression showing \frac{5{b} to the power of 2 square root of 15c - csquare root of 15}{3{b} to the power of 2 {c} to the power of 2 }
f A LaTex expression showing \frac{5{b} to the power of 2 square root of 5 + square root of 5c}{3{b} to the power of 2 c}
4
Divide the radical expressions and simplify the answer
A LaTex expression showing \frac{3rsquare root of 3x + xsquare root of 11x}{rxsquare root of 5r}
a A LaTex expression showing \frac{3rsquare root of 15rx - xsquare root of 55r{x to the power of -1 }}{5x}
b A LaTex expression showing \frac{3square root of 15rx + xsquare root of 55rx}{5r}
c A LaTex expression showing \frac{3rsquare root of 15rx + xsquare root of 55rx}{5{r} to the power of 2 x}
d A LaTex expression showing \frac{3rsquare root of 15r + xsquare root of 55rx}{5{r} to the power of 3 x}
e A LaTex expression showing \frac{3r{x} to the power of -2 square root of 15rx + xsquare root of 55rx}{5{r} to the power of 2 {x} to the power of 2 }
f A LaTex expression showing \frac{3rsquare root of 15rx + xsquare root of 55rx}{5x}
5
Divide the radical expressions and simplify the answer
A LaTex expression showing \frac{2rsquare root of 7rp - {p} to the power of 2 square root of 2}{rpsquare root of 3r}
a A LaTex expression showing \frac{2{r} to the power of 2 square root of 21p + {p} to the power of 2 square root of 6}{3{r} to the power of 3 p}
b A LaTex expression showing \frac{2{r} to the power of 2 square root of 21p - {p} to the power of 2 square root of 6r}{3{r} to the power of 2 p}
c A LaTex expression showing \frac{2{r} to the power of 2 square root of p - {p} to the power of 2 square root of 6r}{3{r} to the power of 2 p}
d A LaTex expression showing \frac{2{r} to the power of 2 square root of 3p + {p} to the power of 2 square root of 6r}{{r} to the power of 2 p}
e A LaTex expression showing \frac{2rsquare root of 21p + {p} to the power of 2 square root of 6r}{rp}
f A LaTex expression showing \frac{2rsquare root of 21p + {p} to the power of 2 square root of 6r}{3r{p} to the power of -1 }
6
Divide the radical expressions and simplify the answer
A LaTex expression showing \frac{4mnsquare root of 7 + mnsquare root of 3n}{{m} to the power of 2 square root of 2n}
a A LaTex expression showing \frac{4square root of 14n + nsquare root of 6}{2m}
b A LaTex expression showing \frac{square root of 14n - nsquare root of 6}{m}
c A LaTex expression showing \frac{4nsquare root of 14n + nsquare root of 6}{2m}
d A LaTex expression showing \frac{4square root of 14n + nsquare root of 3}{2m}
e A LaTex expression showing \frac{2square root of 14n + nsquare root of 6}{2m{n} to the power of -2 }
f A LaTex expression showing \frac{2square root of 14n + nsquare root of 6}{m}
7
Divide the radical expressions and simplify the answer
A LaTex expression showing \frac{2psquare root of 13 - {x} to the power of 2 square root of 11p}{psquare root of 7}
a A LaTex expression showing \frac{2p + {x} to the power of 2 square root of 77p}{7}
b A LaTex expression showing \frac{2psquare root of 91 - {x} to the power of 2 square root of p}{7{p} to the power of 2 }
c A LaTex expression showing \frac{psquare root of 91 - {x} to the power of 2 square root of 77p}{p}
d A LaTex expression showing \frac{2p - {x} to the power of 2 square root of 77p}{7{p} to the power of 3 }
e A LaTex expression showing \frac{2{p} to the power of 3 square root of 91 - {x} to the power of 2 square root of 77p}{7}
f A LaTex expression showing \frac{2psquare root of 91 - {x} to the power of 2 square root of 77p}{7p}