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 32 times square root of 45{z to the power of 4 }
a A LaTex expression showing 12{z} to the power of 3 square root of 10
b A LaTex expression showing {z} to the power of 2
c A LaTex expression showing 12{z} to the power of 2 square root of 10
d A LaTex expression showing 12zsquare root of 10z
e A LaTex expression showing 12zsquare root of 10
2
Multiply the radical expressions and simplify the answer
A LaTex expression showing square root of 176{m to the power of 2 {r} to the power of 3 } times square root of 20r
a A LaTex expression showing 8m{r} to the power of 2 square root of 55
b A LaTex expression showing 8m{r} to the power of 3 square root of 55
c A LaTex expression showing 8m{r} to the power of 2
d A LaTex expression showing 8m{r} to the power of 2 square root of 55m
3
Multiply the radical expressions and simplify the answer
A LaTex expression showing square root of 50p{d to the power of 4 } times square root of 75{p to the power of 2 }
a A LaTex expression showing 25pdsquare root of 6p
b A LaTex expression showing 25p{d} to the power of 2 square root of p
c A LaTex expression showing 25p{d} to the power of 3 square root of 6p
d A LaTex expression showing p{d} to the power of 2 square root of p
e A LaTex expression showing 25p{d} to the power of 2 square root of 6p
4
Multiply the radical expressions and simplify the answer
A LaTex expression showing square root of 28{z to the power of 4 {y} to the power of 3 } times square root of 50{z to the power of 3 {y} to the power of 3 }
a A LaTex expression showing 10{z} to the power of 3 {y} to the power of 3 square root of 14zy
b A LaTex expression showing 10{z} to the power of 3 {y} to the power of 3 square root of 14
c A LaTex expression showing 10{z} to the power of 3 {y} to the power of 3 square root of 14z
d A LaTex expression showing 10{z} to the power of 2 {y} to the power of 3 square root of 14z
5
Multiply the radical expressions and simplify the answer
A LaTex expression showing square root of 44y times square root of 32{p to the power of 4 {y} to the power of 2 }
a A LaTex expression showing 8y{p} to the power of 2 square root of 22
b A LaTex expression showing 8{y} to the power of 2 {p} to the power of 2 square root of 22
c A LaTex expression showing 8y{p} to the power of 2 square root of y
d A LaTex expression showing y{p} to the power of 2 square root of y
e A LaTex expression showing 8y{p} to the power of 2 square root of 22y
6
Multiply the radical expressions and simplify the answer
A LaTex expression showing square root of 20{y to the power of 2 {p} to the power of 2 } times square root of 52{y to the power of 4 {p} to the power of 4 }
a A LaTex expression showing 8{y} to the power of 3 {p} to the power of 3 square root of 65
b A LaTex expression showing 4{y} to the power of 3 {p} to the power of 4 square root of 65
c A LaTex expression showing 4{y} to the power of 3 {p} to the power of 3 square root of 65p
d A LaTex expression showing 4{y} to the power of 3 {p} to the power of 2 square root of 65p
e A LaTex expression showing 4{y} to the power of 3 {p} to the power of 3 square root of 65
7
Multiply the radical expressions and simplify the answer
A LaTex expression showing square root of 32{p to the power of 3 b} times square root of 8
a A LaTex expression showing 16psquare root of p
b A LaTex expression showing 16pbsquare root of pb
c A LaTex expression showing 16psquare root of pb
d A LaTex expression showing 16square root of pb