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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Radicals - Multiplying Monomials (Values and Variables)
1
Multiply the radical expressions and simplify the answer
A LaTex expression showing square root of 8{m to the power of 3 {r} to the power of 3 } times square root of 27{m to the power of 2 {r} to the power of 2 }
a A LaTex expression showing 6{m} to the power of 2 {r} to the power of 2 square root of 6r
b A LaTex expression showing 6{m} to the power of 2 {r} to the power of 2 square root of 6mr
c A LaTex expression showing 6{m} to the power of 2 rsquare root of 6mr
d A LaTex expression showing 6{m} to the power of 2 {r} to the power of 2 square root of mr
e A LaTex expression showing 6{m} to the power of 2 {r} to the power of 3 square root of 6m
2
Multiply the radical expressions and simplify the answer
A LaTex expression showing square root of 52{z to the power of 4 {x} to the power of 3 } times square root of 32{z to the power of 2 {x} to the power of 4 }
a A LaTex expression showing 8{z} to the power of 3 {x} to the power of 4 square root of 26
b A LaTex expression showing 8{z} to the power of 2 {x} to the power of 3 square root of 26x
c A LaTex expression showing 8{z} to the power of 3 {x} to the power of 3 square root of x
d A LaTex expression showing 8{z} to the power of 3 {x} to the power of 3 square root of 26x
e A LaTex expression showing 8{z} to the power of 3 {x} to the power of 2 square root of 26x
3
Multiply the radical expressions and simplify the answer
A LaTex expression showing square root of 8p{t to the power of 4 } times square root of 176{p to the power of 3 }
a A LaTex expression showing {p} to the power of 2 {t} to the power of 2
b A LaTex expression showing 8{p} to the power of 2 {t} to the power of 2 square root of 22
c A LaTex expression showing 8{p} to the power of 2 tsquare root of 22t
d A LaTex expression showing 8{p} to the power of 2 {t} to the power of 2 square root of 22t
4
Multiply the radical expressions and simplify the answer
A LaTex expression showing square root of 117{r to the power of 3 {p} to the power of 3 } times square root of 27{r to the power of 3 {p} to the power of 2 }
a A LaTex expression showing 9{r} to the power of 2 {p} to the power of 2 square root of 39rp
b A LaTex expression showing 9{r} to the power of 3 {p} to the power of 3 square root of 39
c A LaTex expression showing 9{r} to the power of 3 psquare root of 39p
d A LaTex expression showing 9{r} to the power of 3 {p} to the power of 3 square root of 39p
e A LaTex expression showing 9{r} to the power of 3 {p} to the power of 2 square root of 39p
5
Multiply the radical expressions and simplify the answer
A LaTex expression showing square root of 52{q to the power of 2 } times square root of 48q
a A LaTex expression showing 8{q} to the power of 2 square root of 39
b A LaTex expression showing 24qsquare root of 39q
c A LaTex expression showing 8{q} to the power of 2 square root of 39q
d A LaTex expression showing 8qsquare root of 39
e A LaTex expression showing 8qsquare root of 39q
6
Multiply the radical expressions and simplify the answer
A LaTex expression showing square root of 28{z to the power of 2 {p} to the power of 4 } times square root of 75p
a A LaTex expression showing 10z{p} to the power of 2 square root of p
b A LaTex expression showing 50z{p} to the power of 2 square root of 21p
c A LaTex expression showing 10{p} to the power of 2 square root of 21p
d A LaTex expression showing z{p} to the power of 2 square root of p
e A LaTex expression showing 10z{p} to the power of 2 square root of 21p
7
Multiply the radical expressions and simplify the answer
A LaTex expression showing square root of 27{m to the power of 4 } times square root of 12{m to the power of 4 {y} to the power of 4 }
a A LaTex expression showing 18{m} to the power of 4 {y} to the power of 2
b A LaTex expression showing 18{m} to the power of 3 {y} to the power of 2
c A LaTex expression showing 18{m} to the power of 4 {y} to the power of 3
d A LaTex expression showing 18{m} to the power of 5 {y} to the power of 2
8
Multiply the radical expressions and simplify the answer
A LaTex expression showing square root of 99{q to the power of 3 y} times square root of 8{q to the power of 4 y}
a A LaTex expression showing 6{q} to the power of 3 {y} to the power of 2 square root of 22q
b A LaTex expression showing 6{q} to the power of 3 ysquare root of 22q
c A LaTex expression showing 6{q} to the power of 3 ysquare root of 22qy
d A LaTex expression showing 6{q} to the power of 4 ysquare root of 22q
e A LaTex expression showing 6{q} to the power of 2 ysquare root of 22q