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Radicals

Divide Binomials by Monomials (Values and Variables) (Level 2)

This math topic focuses on the division of radical expressions, specifically dividing binomials by monomials that include both values and variables. It is a part of a broader unit on introductory division of radicals. The problems involve simplifying expressions under the radical and can include combining like terms or manipulating powers and coefficients within the radical and across the rational expression. It teaches how to simplify complex radical expressions through division, blending algebraic manipulation with radical expression rules. The worksheet likely includes step-by-step problems to develop the skills necessary for handling radicals in algebra.

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

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

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Radicals - Divide Binomials by Monomials (Values and Variables)
1
Divide the radical expressions and simplify the answer
A LaTex expression showing \frac{square root of 11z + zsquare root of 3z}{zsquare root of 7}
a A LaTex expression showing \frac{square root of 77 + zsquare root of 21z}{7{z} to the power of 2 }
b A LaTex expression showing \frac{square root of 77z + zsquare root of 21z}{7z}
c A LaTex expression showing \frac{square root of 77z - {z} to the power of 2 square root of 21z}{7}
d A LaTex expression showing \frac{square root of 77z + {z} to the power of 3 square root of 21z}{14z}
e A LaTex expression showing \frac{square root of 77{z to the power of -1 } - zsquare root of 21z}{7{z} to the power of 3 }
2
Divide the radical expressions and simplify the answer
A LaTex expression showing \frac{dsquare root of 2d + square root of 11d}{square root of 11d}
a A LaTex expression showing dsquare root of 22 - 1
b A LaTex expression showing \frac{dsquare root of 22 + 11}{11}
c A LaTex expression showing \frac{{d} to the power of 3 square root of 22 - 11}{4}
d A LaTex expression showing \frac{dsquare root of 22 + 11}{5}
e A LaTex expression showing dsquare root of 22 + 5
3
Divide the radical expressions and simplify the answer
A LaTex expression showing \frac{{y} to the power of 2 square root of 3 + square root of 3}{{y} to the power of 2 square root of 2}
a A LaTex expression showing \frac{{y} to the power of 2 square root of 6 + square root of 6}{2{y} to the power of 2 }
b A LaTex expression showing \frac{{y} to the power of 2 square root of 2 - square root of 2}{2{y} to the power of 2 }
c A LaTex expression showing \frac{{y} to the power of 2 square root of 3 + square root of 6}{{y} to the power of 2 }
d A LaTex expression showing \frac{{y} to the power of 2 square root of 6 + 5square root of 6}{{y} to the power of 2 }
4
Divide the radical expressions and simplify the answer
A LaTex expression showing \frac{msquare root of 2 - msquare root of 7}{square root of 2}
a A LaTex expression showing \frac{2m - msquare root of 14}{2}
b A LaTex expression showing \frac{2msquare root of 2 + msquare root of 14}{4}
c A LaTex expression showing \frac{2m + msquare root of 14}{5}
d A LaTex expression showing 3m
e A LaTex expression showing \frac{5m - msquare root of 14}{2}
5
Divide the radical expressions and simplify the answer
A LaTex expression showing \frac{bsquare root of 2b - square root of 7}{{b} to the power of 2 square root of 2}
a A LaTex expression showing \frac{4bsquare root of b + square root of 14}{4{b} to the power of 2 }
b A LaTex expression showing \frac{2b + square root of 14}{2}
c A LaTex expression showing \frac{2bsquare root of b - square root of 14}{2{b} to the power of 2 }
d A LaTex expression showing \frac{2square root of b - square root of 14}{{b} to the power of 2 }
e A LaTex expression showing \frac{2{b} to the power of -1 square root of b + square root of 14}{2{b} to the power of 4 }
6
Divide the radical expressions and simplify the answer
A LaTex expression showing \frac{nsquare root of 11n + {n} to the power of 2 square root of 7}{nsquare root of 3n}
a A LaTex expression showing \frac{square root of 11 - nsquare root of 7}{3}
b A LaTex expression showing \frac{square root of 33 + square root of 21n}{4}
c A LaTex expression showing square root of 33 + nsquare root of 21n
d A LaTex expression showing \frac{square root of 33 + 4square root of 21n}{3}
e A LaTex expression showing \frac{square root of 33 + square root of 21n}{3}
7
Divide the radical expressions and simplify the answer
A LaTex expression showing \frac{square root of 11x + square root of 5x}{square root of 3}
a A LaTex expression showing \frac{square root of 33x - square root of 15}{3}
b A LaTex expression showing \frac{square root of 33 - square root of 15x}{4}
c A LaTex expression showing \frac{square root of 33x + square root of 15x}{3}
d A LaTex expression showing \frac{xsquare root of 33x - square root of 15x}{2}
e A LaTex expression showing square root of 33{x to the power of -1 } + square root of 15x
8
Divide the radical expressions and simplify the answer
A LaTex expression showing \frac{ysquare root of 2y + square root of 7}{ysquare root of 2y}
a A LaTex expression showing \frac{2{y} to the power of 2 + square root of 14y}{2{y} to the power of 2 }
b A LaTex expression showing \frac{2{y} to the power of 2 - square root of 14y}{2{y} to the power of 3 }
c A LaTex expression showing \frac{{y} to the power of 2 + square root of 14y}{2{y} to the power of 2 }
d A LaTex expression showing \frac{2y + square root of 14y}{2y}
e A LaTex expression showing \frac{2{y} to the power of 3 + square root of 14y}{2{y} to the power of 3 }