Radicals

Multiplying Monomials (Values and Variables) (Level 2)

This math topic focuses on the skill of multiplying monomial radical expressions and simplifying the results. It's part of a broader introduction to radical multiplication. The problems involve manipulating both numerical and variable components within radical signs. Each question presents a multiplication problem involving square roots of expressions that include both constants and powers of variables. Multiple-choice answers demonstrate different potential steps or missteps in simplification, illustrating how to accurately combine and simplify radical terms according to the properties of exponents and radicals.

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 27r times square root of 75{r to the power of 2 }
a A LaTex expression showing 45rsquare root of r
b A LaTex expression showing 45{r} to the power of 2
c A LaTex expression showing 45{r} to the power of 2 square root of r
d A LaTex expression showing 45r
2
Multiply the radical expressions and simplify the answer
A LaTex expression showing square root of 32r times square root of 8r
a A LaTex expression showing 16r
b A LaTex expression showing 48r
c A LaTex expression showing r
d A LaTex expression showing 16{r} to the power of 2
e A LaTex expression showing 16
3
Multiply the radical expressions and simplify the answer
A LaTex expression showing square root of 44{t to the power of 2 } times square root of 99{t to the power of 4 }
a A LaTex expression showing {t} to the power of 3
b A LaTex expression showing 198{t} to the power of 3
c A LaTex expression showing 66{t} to the power of 3
d A LaTex expression showing 66{t} to the power of 2 square root of t
4
Multiply the radical expressions and simplify the answer
A LaTex expression showing square root of 75{y to the power of 2 } times square root of 27{y to the power of 2 }
a A LaTex expression showing 45{y} to the power of 3
b A LaTex expression showing 45{y} to the power of 2
c A LaTex expression showing 45ysquare root of y
5
Multiply the radical expressions and simplify the answer
A LaTex expression showing square root of 50{r to the power of 4 } times square root of 18{r to the power of 3 }
a A LaTex expression showing 30{r} to the power of 3
b A LaTex expression showing 120{r} to the power of 3 square root of r
c A LaTex expression showing 30{r} to the power of 3 square root of r
6
Multiply the radical expressions and simplify the answer
A LaTex expression showing square root of 48{x to the power of 3 } times square root of 27{x to the power of 3 }
a A LaTex expression showing 36{x} to the power of 3 square root of x
b A LaTex expression showing 36{x} to the power of 4
c A LaTex expression showing 36{x} to the power of 2 square root of x
d A LaTex expression showing 36{x} to the power of 3
7
Multiply the radical expressions and simplify the answer
A LaTex expression showing square root of 32{q to the power of 3 } times square root of 50{q to the power of 2 }
a A LaTex expression showing 120{q} to the power of 2 square root of q
b A LaTex expression showing 40{q} to the power of 2 square root of q
c A LaTex expression showing 80{q} to the power of 2 square root of q
d A LaTex expression showing 40{q} to the power of 3 square root of q
8
Multiply the radical expressions and simplify the answer
A LaTex expression showing square root of 50{t to the power of 3 } times square root of 32{t to the power of 4 }
a A LaTex expression showing 40{t} to the power of 3 square root of t
b A LaTex expression showing 40{t} to the power of 4 square root of t
c A LaTex expression showing 40{t} to the power of 3
d A LaTex expression showing 40{t} to the power of 4