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Radical

Divide Binomials by Monomials (Values and Variables) (Level 1)

This math topic focuses on dividing radical expressions where binomials are divided by monomials, involving both numerical and algebraic expressions. The problems require simplification of the resulting expressions following the division. Each question presents a radical binomial expression in the numerator and a monomial in the denominator. Multiple-choice answers suggest the students need to select the correct simplified form, highlighting skills in manipulating square roots, variables, and rationalizing the denominator where applicable.

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)

Complete these online problems with 80% or 4 correct answers in a row. Results are immediate.

Divide the radical expressions and simplify the answer

13y−5y2y3\frac{\sqrt{13y} - 5{y}^{2}}{y\sqrt{3}}

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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 1)'. 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{dsquare root of 5 + 4}{square root of 2d}
a A LaTex expression showing \frac{dsquare root of 10d + 4dsquare root of 2}{2}
b A LaTex expression showing \frac{dsquare root of 10d + 4square root of 2d}{2{d} to the power of -1 }
c A LaTex expression showing \frac{dsquare root of 10{d to the power of -1 } + 4square root of 2d}{2{d} to the power of 2 }
d A LaTex expression showing \frac{dsquare root of 10d + 3square root of 2d}{2d}
e A LaTex expression showing \frac{dsquare root of 10d + square root of 2d}{2{d} to the power of -1 }
f A LaTex expression showing \frac{dsquare root of 10d + 4square root of 2d}{2d}
2
Divide the radical expressions and simplify the answer
A LaTex expression showing \frac{square root of 11p - 4psquare root of p}{{p} to the power of 2 square root of 3}
a A LaTex expression showing \frac{square root of 33p - 4{p} to the power of 3 square root of 3p}{{p} to the power of 2 }
b A LaTex expression showing \frac{square root of 33p - 4{p} to the power of -1 square root of 3p}{{p} to the power of 2 }
c A LaTex expression showing \frac{square root of 33p - 4psquare root of p}{{p} to the power of 2 }
d A LaTex expression showing \frac{square root of 33p - 4psquare root of p}{4{p} to the power of 2 }
e A LaTex expression showing \frac{square root of 33p + 4psquare root of 3p}{5{p} to the power of 2 }
f A LaTex expression showing \frac{square root of 33p - 4psquare root of 3p}{3{p} to the power of 2 }
3
Divide the radical expressions and simplify the answer
A LaTex expression showing \frac{2c + {c} to the power of 2 square root of 5}{square root of 2c}
a A LaTex expression showing \frac{2square root of 2c + csquare root of 10c}{2}
b A LaTex expression showing 2csquare root of 2 + csquare root of 10c
c A LaTex expression showing \frac{2square root of 2 - csquare root of 10c}{5}
d A LaTex expression showing \frac{2square root of 2c - {c} to the power of 2 square root of 10c}{4}
e A LaTex expression showing \frac{2square root of 2c - csquare root of 10c}{4}
f A LaTex expression showing 2square root of 2 + csquare root of 10c
4
Divide the radical expressions and simplify the answer
A LaTex expression showing \frac{3{x} to the power of 2 + square root of 13x}{xsquare root of 2x}
a A LaTex expression showing \frac{3xsquare root of 2x + square root of 3}{x}
b A LaTex expression showing \frac{3square root of 2x + square root of 26}{4x}
c A LaTex expression showing \frac{3xsquare root of 2 + square root of 26}{2{x} to the power of 3 }
d A LaTex expression showing \frac{3xsquare root of 2x + square root of 2}{2{x} to the power of 2 }
e A LaTex expression showing \frac{3xsquare root of 2x + square root of 26}{2x}
f A LaTex expression showing \frac{3{x} to the power of 2 square root of 2x + square root of 26}{2}
5
Divide the radical expressions and simplify the answer
A LaTex expression showing \frac{{p} to the power of 2 square root of 13 - 4square root of p}{square root of 11}
a A LaTex expression showing \frac{{p} to the power of 2 square root of 143 + 4psquare root of 11}{5}
b A LaTex expression showing \frac{{p} to the power of 2 square root of 143 - 4square root of 11p}{11}
c A LaTex expression showing {p} to the power of 3 square root of 143 + 4square root of 11p
d A LaTex expression showing \frac{{p} to the power of 4 square root of 143 - 4square root of 11p}{11}
e A LaTex expression showing \frac{{p} to the power of 2 square root of 143 - 5square root of 11p}{3}
f A LaTex expression showing 3{p} to the power of 2 square root of 143 + 4square root of 11p
6
Divide the radical expressions and simplify the answer
A LaTex expression showing \frac{{d} to the power of 2 square root of 7 + 2d}{dsquare root of 7}
a A LaTex expression showing 7d + 5square root of 7
b A LaTex expression showing 7d + square root of 7
c A LaTex expression showing \frac{7{d} to the power of -1 - 2square root of 7}{7}
d A LaTex expression showing \frac{7{d} to the power of 2 + 2square root of 7}{4}
e A LaTex expression showing \frac{7d + 2square root of 7}{7}
f A LaTex expression showing 7{d} to the power of -1 - 2square root of 7
7
Divide the radical expressions and simplify the answer
A LaTex expression showing \frac{5square root of m + msquare root of 13m}{square root of 5m}
a A LaTex expression showing 5 + msquare root of 65
b A LaTex expression showing \frac{square root of 10 - msquare root of 130}{10}
c A LaTex expression showing \frac{5 + msquare root of 65}{2}
d A LaTex expression showing \frac{5square root of 5 + msquare root of 65}{5}
e A LaTex expression showing \frac{5square root of 5 - m}{5}
f A LaTex expression showing \frac{5 + msquare root of 65}{10}