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Radicals

Divide Binomials (Values Only) (Level 1)

This math topic focuses on dividing binomial expressions containing radicals and simplifying the results. It includes various problems where students are tasked to divide expressions under a radical and choose the correct simplified form from multiple options. The expressions primarily involve square roots combined with integer terms. The main objective is to practice manipulating and simplifying radical expressions involving division of binomials, enhancing skills in algebraic manipulation of roots and rational expressions.

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{2 - square root of 5}{2 - square root of 7}
a A LaTex expression showing \frac{4 + 2square root of 7 - 2square root of 5 + 2}{-3}
b A LaTex expression showing \frac{4 + square root of 7 - 2square root of 5 - 2square root of 35}{2}
c A LaTex expression showing \frac{4 + 2square root of 7 - 2square root of 5 - square root of 35}{-3}
d A LaTex expression showing \frac{4 + 2square root of 7 - 2square root of 5 - square root of 35}{-3square root of 3}
e A LaTex expression showing \frac{1 + 2square root of 7 - 2square root of 5 + square root of 35}{3}
2
Divide the radical expressions and simplify the answer
A LaTex expression showing \frac{3 - square root of 11}{square root of 5 - 3}
a A LaTex expression showing \frac{3square root of 5 - 9 - 2square root of 55 + 3square root of 11}{-4}
b A LaTex expression showing 3square root of 5 + 1 - square root of 55 - 3square root of 11
c A LaTex expression showing \frac{3square root of 5 + 9square root of 2 - square root of 55 - square root of 11}{5}
d A LaTex expression showing \frac{3square root of 5 + 9 - square root of 55 - 3square root of 11}{-4}
e A LaTex expression showing 3square root of 5 + 9 - square root of 55 + 3
3
Divide the radical expressions and simplify the answer
A LaTex expression showing \frac{4 + square root of 7}{4 + square root of 7}
a A LaTex expression showing 1
b A LaTex expression showing square root of 4
c A LaTex expression showing 5 over square root of 4
d A LaTex expression showing 1 over square root of 2
4
Divide the radical expressions and simplify the answer
A LaTex expression showing \frac{2 + square root of 11}{5 + square root of 7}
a A LaTex expression showing \frac{10 - square root of 7 + square root of 11 - square root of 77}{18}
b A LaTex expression showing \frac{10 - square root of 7 - 3square root of 11 - square root of 77}{18}
c A LaTex expression showing 4 - 2square root of 7 + 5square root of 11 + 1
d A LaTex expression showing 10 - 2square root of 7 + 5square root of 11 - 3square root of 77
e A LaTex expression showing \frac{10 - 2square root of 7 + 5square root of 11 - square root of 77}{18}
5
Divide the radical expressions and simplify the answer
A LaTex expression showing \frac{3 + square root of 11}{square root of 7 + 2}
a A LaTex expression showing \frac{3square root of 7 - 6 + square root of 77 - 2square root of 11}{3}
b A LaTex expression showing 3square root of 7 - 6 + square root of 77 - square root of 2
c A LaTex expression showing \frac{4 + 6 + square root of 77 - 2square root of 11}{5}
d A LaTex expression showing \frac{3square root of 7 - 6 + 5square root of 77 - 3square root of 11}{3}
e A LaTex expression showing \frac{square root of 7 + 6 - square root of 77 - 2}{4}
6
Divide the radical expressions and simplify the answer
A LaTex expression showing \frac{2 - square root of 5}{4 - square root of 3}
a A LaTex expression showing 1 + 2square root of 3 - 4square root of 5 - square root of 15
b A LaTex expression showing \frac{8 - square root of 3 + 4square root of 5 - square root of 15}{13}
c A LaTex expression showing 1 + 2 - 4square root of 5 - square root of 15
d A LaTex expression showing \frac{8 + 2square root of 3 - 4square root of 5 - square root of 15}{13}
e A LaTex expression showing 8 + square root of 3 - square root of 5 - square root of 15
7
Divide the radical expressions and simplify the answer
A LaTex expression showing \frac{4 + square root of 7}{4 - square root of 3}
a A LaTex expression showing 1 - 4square root of 3 + 4square root of 7 + 2square root of 21
b A LaTex expression showing \frac{16 + 4square root of 3 + 4square root of 3 + square root of 21}{3}
c A LaTex expression showing 1 + square root of 3 + 4square root of 7 + square root of 21
d A LaTex expression showing 16 + 3square root of 3 + 3square root of 7 - square root of 21
e A LaTex expression showing \frac{16 + 4square root of 3 + 4square root of 7 + square root of 21}{13}
8
Divide the radical expressions and simplify the answer
A LaTex expression showing \frac{2 - square root of 11}{square root of 13 + 5}
a A LaTex expression showing \frac{2square root of 13 - 1 - square root of 143 + 5}{-12}
b A LaTex expression showing \frac{2square root of 13 - 10 - square root of 143 + 5square root of 11}{-12}
c A LaTex expression showing \frac{2square root of 13 - 1 - square root of 143 + 5}{2}
d A LaTex expression showing 2square root of 13 - 3 - square root of 143 + square root of 11
e A LaTex expression showing \frac{2square root of 13 - 10square root of 3 - square root of 143 + 5square root of 11}{3}