Multiplying Monomials (Values and Variables) (Level 3)

This math topic focuses on multiplying monomials involving radicals, where students practice simplifying expressions that combine both numerical coefficients and variables under the radical sign. Each problem presents a pair of radical expressions to be multiplied, and students need to simplify the product to the most basic form given multiple-choice answers. Skills practiced include multiplying coefficients and exponents and simplifying radicals. This is part of a broader introduction to multiplication with radicals, geared toward enhancing students' algebraic manipulation skills with roots and powers.

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

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Radicals - Multiplying Monomials (Values and Variables) Worksheet

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Math worksheet on 'Radicals - Multiplying Monomials (Values and Variables) (Level 3)'. Part of a broader unit on 'Radicals - Multiplication Intro' Learn online: app.mobius.academy/math/units/radicals_multiplication_intro/
1
Multiply the radical expressions and simplify the answer
A LaTex expression showing square root of 8{z to the power of 2 {r} to the power of 3 } times square root of 112{z to the power of 2 {r} to the power of 4 }
a A LaTex expression showing 8{z} to the power of 2 {r} to the power of 3 square root of 14r
b A LaTex expression showing 8{z} to the power of 2 {r} to the power of 2 square root of 14r
c A LaTex expression showing {z} to the power of 2 {r} to the power of 3 square root of r
d A LaTex expression showing 40{z} to the power of 2 {r} to the power of 3 square root of 14r
2
Multiply the radical expressions and simplify the answer
A LaTex expression showing square root of 75{p to the power of 4 {x} to the power of 2 } times square root of 32{p to the power of 2 }
a A LaTex expression showing 20{p} to the power of 3 {x} to the power of 2 square root of 6
b A LaTex expression showing {p} to the power of 3 x
c A LaTex expression showing 20{p} to the power of 3 xsquare root of 6
d A LaTex expression showing 20{p} to the power of 3 square root of 6
3
Multiply the radical expressions and simplify the answer
A LaTex expression showing square root of 80{r to the power of 3 b} times square root of 20{r to the power of 2 {b} to the power of 4 }
a A LaTex expression showing 40{r} to the power of 2 {b} to the power of 3 square root of r
b A LaTex expression showing 40{r} to the power of 2 {b} to the power of 2 square root of r
c A LaTex expression showing 40{r} to the power of 2 {b} to the power of 2 square root of rb
d A LaTex expression showing {r} to the power of 2 {b} to the power of 2 square root of rb
4
Multiply the radical expressions and simplify the answer
A LaTex expression showing square root of 32{c to the power of 3 } times square root of 125{n to the power of 3 }
a A LaTex expression showing 60cnsquare root of 10cn
b A LaTex expression showing 40cnsquare root of 10cn
c A LaTex expression showing 20c{n} to the power of 2 square root of 10cn
d A LaTex expression showing 20cnsquare root of 10cn
5
Multiply the radical expressions and simplify the answer
A LaTex expression showing square root of 44{c to the power of 3 } times square root of 27
a A LaTex expression showing 6{c} to the power of 2 square root of 33
b A LaTex expression showing 6square root of 33c
c A LaTex expression showing csquare root of c
d A LaTex expression showing 6csquare root of 33c
6
Multiply the radical expressions and simplify the answer
A LaTex expression showing square root of 112{r to the power of 2 } times square root of 44{r to the power of 4 m}
a A LaTex expression showing {r} to the power of 3 square root of m
b A LaTex expression showing 8{r} to the power of 3 square root of 77rm
c A LaTex expression showing 8{r} to the power of 3 square root of 77
d A LaTex expression showing 8{r} to the power of 3 square root of 77m
e A LaTex expression showing 32{r} to the power of 3 square root of 77m
7
Multiply the radical expressions and simplify the answer
A LaTex expression showing square root of 8{r to the power of 2 {c} to the power of 3 } times square root of 125r{c to the power of 3 }
a A LaTex expression showing 10r{c} to the power of 2 square root of 10r
b A LaTex expression showing 10{c} to the power of 3 square root of 10r
c A LaTex expression showing 10r{c} to the power of 3 square root of 10r
Radicals - Multiplying Monomials (Values and Variables) (Level 3) - Mobius Math