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Radicals

Divide Binomials (Values Only) (Level 2)

This math topic focuses on dividing binomials with radicals and simplifying the results. It is part of an introduction to division involving radicals. The problems require students to divide expressions containing square roots, represented by various binomial formats, and then identify the correct simplified form from multiple choices. Techniques likely practiced include rationalizing denominators and combining like terms within radical expressions. The skills emphasized are crucial for understanding higher-level algebra involving radicals and their operations.

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

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Radicals - Divide Binomials (Values Only) Worksheet

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Radicals - Divide Binomials (Values Only)
1
Divide the radical expressions and simplify the answer
A LaTex expression showing \frac{square root of 5 + square root of 2}{square root of 5 - square root of 11}
a A LaTex expression showing \frac{2 + square root of 55 + square root of 10 + square root of 22}{-6square root of 3}
b A LaTex expression showing \frac{5 + 5square root of 55 + square root of 10 + square root of 22}{-6}
c A LaTex expression showing \frac{2 + 3square root of 55 + square root of 10 - square root of 22}{4}
d A LaTex expression showing \frac{1 + square root of 55 - square root of 10 + square root of 22}{-6}
e A LaTex expression showing \frac{5 + square root of 55 + square root of 10 + square root of 22}{-6}
2
Divide the radical expressions and simplify the answer
A LaTex expression showing \frac{square root of 7 - square root of 5}{square root of 2 - square root of 13}
a A LaTex expression showing \frac{1 + square root of 91 - square root of 10 + square root of 65}{-11square root of 4}
b A LaTex expression showing \frac{square root of 14 + 2square root of 91 - square root of 10 + 1}{4}
c A LaTex expression showing square root of 14 + square root of 91 - 3square root of 10 - 5square root of 65
d A LaTex expression showing \frac{square root of 14 + 1 + square root of 10 - square root of 65}{-11}
e A LaTex expression showing \frac{square root of 14 + square root of 91 - square root of 10 - square root of 65}{-11}
3
Divide the radical expressions and simplify the answer
A LaTex expression showing \frac{square root of 11 + square root of 7}{square root of 13 + square root of 7}
a A LaTex expression showing \frac{square root of 143 - square root of 77 + square root of 91 - 7}{6}
b A LaTex expression showing 1 - 1 + square root of 91 + 7
c A LaTex expression showing \frac{square root of 143 - square root of 77 + 3square root of 91 - 7}{5}
d A LaTex expression showing square root of 143 + square root of 77 + 2square root of 91 - 7
e A LaTex expression showing square root of 143 + square root of 77 + square root of 91 - 7
4
Divide the radical expressions and simplify the answer
A LaTex expression showing \frac{square root of 11 + square root of 13}{square root of 5 + square root of 7}
a A LaTex expression showing square root of 55 - 4square root of 77 + square root of 65 - 1
b A LaTex expression showing \frac{square root of 55 + square root of 77 + 1 - square root of 91}{-2}
c A LaTex expression showing \frac{square root of 55 - square root of 77 + square root of 65 - square root of 91}{-2}
d A LaTex expression showing \frac{square root of 55 - 1 + square root of 65 - square root of 91}{-2square root of 4}
e A LaTex expression showing \frac{square root of 55 + square root of 77 + 1 - square root of 91}{5}
5
Divide the radical expressions and simplify the answer
A LaTex expression showing \frac{square root of 11 + square root of 11}{square root of 2 - square root of 7}
a A LaTex expression showing square root of 22 + 2square root of 77
b A LaTex expression showing \frac{square root of 22 + 2square root of 77}{-5square root of 4}
c A LaTex expression showing \frac{square root of 22 + 2square root of 77}{3}
d A LaTex expression showing \frac{2square root of 22 + 2square root of 77}{-5}
e A LaTex expression showing \frac{square root of 22 + 2square root of 77}{-5}
6
Divide the radical expressions and simplify the answer
A LaTex expression showing \frac{square root of 5 - square root of 2}{square root of 2 - square root of 13}
a A LaTex expression showing \frac{square root of 10 + 1 - 2 - square root of 26}{-11square root of 4}
b A LaTex expression showing \frac{square root of 10 + 3square root of 65 - 2 + 2square root of 26}{4}
c A LaTex expression showing square root of 10 + square root of 65 + 2 - square root of 26
d A LaTex expression showing \frac{square root of 10 + square root of 65 - 2 + 5square root of 26}{-11square root of 4}
e A LaTex expression showing \frac{square root of 10 + square root of 65 - 2 - square root of 26}{-11}
7
Divide the radical expressions and simplify the answer
A LaTex expression showing \frac{square root of 2 + square root of 13}{square root of 3 + square root of 2}
a A LaTex expression showing \frac{square root of 6 - 2 + square root of 39 + square root of 26}{5}
b A LaTex expression showing \frac{2square root of 6 + 2 - square root of 39 - square root of 26}{4}
c A LaTex expression showing square root of 6 - 1 + square root of 39 - square root of 26
d A LaTex expression showing square root of 6 - 2 + square root of 39 - square root of 26
e A LaTex expression showing \frac{square root of 6 + 2 + square root of 39 - square root of 26}{4}
8
Divide the radical expressions and simplify the answer
A LaTex expression showing \frac{square root of 5 - square root of 7}{square root of 2 - square root of 5}
a A LaTex expression showing \frac{1 + 1 - square root of 14 + square root of 35}{-3square root of 3}
b A LaTex expression showing \frac{square root of 10 + 5 + square root of 14 - 1}{-3}
c A LaTex expression showing \frac{square root of 10 + 5 - square root of 14 - square root of 35}{-3}
d A LaTex expression showing \frac{square root of 10 + 5 + 3square root of 14 - square root of 35}{-3}
e A LaTex expression showing square root of 10 + 5 - square root of 14 + square root of 35