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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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Math worksheet on 'Radicals - Divide Binomials (Values Only) (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{3 - square root of 11}{square root of 2 + 3}
a A LaTex expression showing \frac{3 - 9 + square root of 22 - 3square root of 2}{-7}
b A LaTex expression showing \frac{3square root of 2 - 9 - 1 + 3square root of 11}{-7square root of 2}
c A LaTex expression showing \frac{3square root of 2 - 9 - square root of 22 + 3square root of 11}{-7}
d A LaTex expression showing 3square root of 2 + 9 - square root of 22 - 3square root of 11
e A LaTex expression showing \frac{3square root of 2 + 1 - square root of 22 + 3}{2}
2
Divide the radical expressions and simplify the answer
A LaTex expression showing \frac{5 - square root of 2}{square root of 3 - 5}
a A LaTex expression showing 5square root of 4 + 25 - square root of 6 - 4square root of 2
b A LaTex expression showing \frac{5square root of 3 + 1 - square root of 6 - 5}{4}
c A LaTex expression showing 5square root of 3 - 1 - square root of 6 + 5square root of 4
d A LaTex expression showing \frac{5square root of 3 + 25 - square root of 6 - 5square root of 2}{-22}
e A LaTex expression showing \frac{5square root of 3 - 25square root of 3 - square root of 6 - square root of 2}{-22}
3
Divide the radical expressions and simplify the answer
A LaTex expression showing \frac{4 + square root of 7}{3 + square root of 7}
a A LaTex expression showing \frac{5 - square root of 7}{2square root of 2}
b A LaTex expression showing \frac{5 - square root of 7}{2}
c A LaTex expression showing 5 - 2square root of 7
d A LaTex expression showing \frac{1 - square root of 7}{4}
4
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 \frac{16 + 4square root of 3 + 4square root of 3 + square root of 21}{3}
b A LaTex expression showing 16 + 3square root of 3 + 3square root of 7 - square root of 21
c A LaTex expression showing 1 + square root of 3 + 4square root of 7 + square root of 21
d A LaTex expression showing 1 - 4square root of 3 + 4square root of 7 + 2square root of 21
e A LaTex expression showing \frac{16 + 4square root of 3 + 4square root of 7 + square root of 21}{13}
5
Divide the radical expressions and simplify the answer
A LaTex expression showing \frac{square root of 13 + 2}{square root of 11 - 2}
a A LaTex expression showing \frac{square root of 143 - 2square root of 13 + 2square root of 11 + 4}{7}
b A LaTex expression showing square root of 143 + 2square root of 13 + square root of 11 + 1
c A LaTex expression showing \frac{square root of 143 + 2square root of 13 + 2square root of 11 + 4}{7}
d A LaTex expression showing square root of 143 + 3square root of 13 + 4square root of 11 - 4
e A LaTex expression showing \frac{1 - 2square root of 13 + 2square root of 11 + 4}{5}
6
Divide the radical expressions and simplify the answer
A LaTex expression showing \frac{2 + square root of 11}{square root of 11 + 3}
a A LaTex expression showing -1square root of 3 + 5
b A LaTex expression showing square root of 11 + 5
c A LaTex expression showing \frac{square root of 11 + 5}{2}
d A LaTex expression showing \frac{-1square root of 11 + 5}{2}
e A LaTex expression showing -1 + 5 over 2
7
Divide the radical expressions and simplify the answer
A LaTex expression showing \frac{3 - square root of 5}{2 - square root of 11}
a A LaTex expression showing \frac{3 - 3square root of 11 - 2square root of 5 - square root of 55}{4}
b A LaTex expression showing 1 + 3square root of 11 - 2square root of 5 - square root of 55
c A LaTex expression showing \frac{6 + 3square root of 11 - 2square root of 5 - square root of 55}{-7}
d A LaTex expression showing \frac{6 + 3square root of 11 - square root of 5 - square root of 55}{-7}
e A LaTex expression showing 6 + 3square root of 11 - 3 - square root of 55