Multiplying Monomials with Binomials (Values and Variables) (Level 2)

This math topic focuses on practicing the multiplication of radicals, specifically multiplying monomials with binomials that involve both values and variables. The content is part of a broader introduction to multiplying radical expressions. Learners are presented with problems where they need to multiply different radical expressions and simplify the results, involving steps like distributing the terms and simplifying using radical rules. Various problem sets challenge learners to multiply and simplify expressions such as square roots that include numerical coefficients and variable terms represented in radical form.

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

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Radicals - Multiplying Monomials with Binomials (Values and Variables) Worksheet

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Radicals - Multiplying Monomials with Binomials (Values and Variables)
1
Multiply the radical expressions and simplify the answer
A LaTex expression showing (bsquare root of 11 - {b} to the power of 2 square root of 11) times {b} to the power of 2 square root of 5
a A LaTex expression showing {b} to the power of 3 square root of 55 - 5{b} to the power of 4 square root of 55
b A LaTex expression showing {b} to the power of 3 square root of 55 - {b} to the power of 6 square root of 55
c A LaTex expression showing {b} to the power of 3 square root of 55 - {b} to the power of 4 square root of 55
d A LaTex expression showing {b} to the power of 2 square root of 55 - {b} to the power of 4 square root of 55
e A LaTex expression showing {b} to the power of 3 square root of 55 - {b} to the power of 4
2
Multiply the radical expressions and simplify the answer
A LaTex expression showing square root of 13z times (square root of 3z - {z} to the power of 2 square root of 2)
a A LaTex expression showing {z} to the power of 2 square root of 39 - {z} to the power of 2 square root of 26z
b A LaTex expression showing zsquare root of 39 - {z} to the power of 3 square root of 26z
c A LaTex expression showing zsquare root of 39 - {z} to the power of 2 square root of 26z
d A LaTex expression showing zsquare root of 39 - {z} to the power of 3 square root of 26
3
Multiply the radical expressions and simplify the answer
A LaTex expression showing (bsquare root of 2b + {b} to the power of 2 square root of 5) times {b} to the power of 2 square root of 13
a A LaTex expression showing {b} to the power of 3 square root of 26 + {b} to the power of 4 square root of 65
b A LaTex expression showing {b} to the power of 3 square root of 26b + {b} to the power of 4 square root of 65
c A LaTex expression showing {b} to the power of 3 square root of 26b + {b} to the power of 2 square root of 65
d A LaTex expression showing {b} to the power of 4 square root of 26 + {b} to the power of 4 square root of 65
4
Multiply the radical expressions and simplify the answer
A LaTex expression showing ({y} to the power of 2 square root of 3 + square root of 7) times square root of 11
a A LaTex expression showing {y} to the power of 2 + square root of 77
b A LaTex expression showing {y} to the power of 2 square root of 33 + 3square root of 77
c A LaTex expression showing {y} to the power of 2 square root of 33 + square root of 77
d A LaTex expression showing {y} to the power of 2 square root of 33 + 1
5
Multiply the radical expressions and simplify the answer
A LaTex expression showing square root of 2 times (square root of 13m - square root of 7)
a A LaTex expression showing square root of 26m - square root of 14
b A LaTex expression showing square root of 26m - 5square root of 14
c A LaTex expression showing square root of 26m - 2
d A LaTex expression showing square root of 26 - square root of 14
6
Multiply the radical expressions and simplify the answer
A LaTex expression showing zsquare root of 2 times (zsquare root of 11z - square root of 3z)
a A LaTex expression showing {z} to the power of 2 square root of 22z - zsquare root of 6
b A LaTex expression showing {z} to the power of 2 square root of 22z - zsquare root of 6z
c A LaTex expression showing {z} to the power of 2 square root of 22 - zsquare root of 6z
d A LaTex expression showing {z} to the power of 2 square root of 22z - {z} to the power of 2 square root of 6z
e A LaTex expression showing {z} to the power of 2 square root of 22z - {z} to the power of -1 square root of 6z
7
Multiply the radical expressions and simplify the answer
A LaTex expression showing (square root of 2 + {c} to the power of 2 square root of 11) times {c} to the power of 2 square root of 3
a A LaTex expression showing {c} to the power of 2 square root of 6 + {c} to the power of 4 square root of 33
b A LaTex expression showing square root of 6 + {c} to the power of 4 square root of 33
c A LaTex expression showing {c} to the power of 2 square root of 6 + {c} to the power of 5 square root of 33
d A LaTex expression showing csquare root of 6 + {c} to the power of 4 square root of 33
8
Multiply the radical expressions and simplify the answer
A LaTex expression showing ({n} to the power of 2 square root of 13 + square root of 3n) times nsquare root of 13
a A LaTex expression showing 13n + nsquare root of 39n
b A LaTex expression showing 13{n} to the power of 3 + nsquare root of 39n
c A LaTex expression showing 13{n} to the power of 3 + nsquare root of 39{n to the power of -1 }
d A LaTex expression showing {n} to the power of 3 + nsquare root of 39n
e A LaTex expression showing 13{n} to the power of 3 + {n} to the power of 2 square root of 39