Multiplying Monomials (Values and Variables) over Fraction (Level 1)

This math topic focuses on practicing the multiplication and simplification of radical expressions involving monomials, both numerical and with variables, often involving fractions. It covers foundational skills necessary to combine and simplify terms under radicals which may include perfect squares and cube roots, along with algebraic manipulation of expressions involving variables raised to different powers. The problems also emphasize simplifying complex radical expressions by utilizing multiplication rules and reducing resulting fractions, key skills in algebra especially with radicals and exponents.

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) over Fraction Worksheet

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Radicals - Multiplying Monomials (Values and Variables) over Fraction
1
A LaTex expression showing \frac{square root of 11{m to the power of 3 } times square root of 176{m to the power of 2 }}{2 over 5 }
Multiply the radical expressions and simplify the answer
a A LaTex expression showing 275msquare root of m
b A LaTex expression showing 110{m} to the power of 2 square root of m
c A LaTex expression showing 44{m} to the power of 2
d A LaTex expression showing 44{m} to the power of 2 square root of m
2
A LaTex expression showing \frac{square root of 176{p to the power of 4 } times square root of 11p}{2 over 4 }
Multiply the radical expressions and simplify the answer
a A LaTex expression showing 44{p} to the power of 2 square root of p
b A LaTex expression showing 44{p} to the power of 2
c A LaTex expression showing 176{p} to the power of 2 square root of p
d A LaTex expression showing 88{p} to the power of 2 square root of p
e A LaTex expression showing 44{p} to the power of 3
3
A LaTex expression showing \frac{square root of 5{r to the power of 3 } times square root of 80}{2 over 4 }
Multiply the radical expressions and simplify the answer
a A LaTex expression showing 20rsquare root of r
b A LaTex expression showing 80square root of r
c A LaTex expression showing 80rsquare root of r
d A LaTex expression showing 40rsquare root of r
e A LaTex expression showing 20{r} to the power of 2 square root of r
4
Multiply the radical expressions and simplify the answer
A LaTex expression showing \frac{square root of 117 times square root of 13}{13 over 2 }
a A LaTex expression showing 6
b A LaTex expression showing 39
5
A LaTex expression showing square root of 117 times square root of 13{d to the power of 3 }
Multiply the radical expressions and simplify the answer
a A LaTex expression showing 39dsquare root of d
b A LaTex expression showing 39{d} to the power of 2
c A LaTex expression showing 39d
d A LaTex expression showing 39{d} to the power of 2 square root of d
6
A LaTex expression showing \frac{square root of 45{y to the power of 2 } times square root of 5y}{5 over 4 }
Multiply the radical expressions and simplify the answer
a A LaTex expression showing 15ysquare root of y
b A LaTex expression showing 75ysquare root of y
c A LaTex expression showing 9ysquare root of y
d A LaTex expression showing 12ysquare root of y
e A LaTex expression showing 60ysquare root of y
7
A LaTex expression showing \frac{square root of 7x times square root of 28{x to the power of 3 }}{7 over 2 }
Multiply the radical expressions and simplify the answer
a A LaTex expression showing {x} to the power of 2
b A LaTex expression showing 14{x} to the power of 2 square root of x
c A LaTex expression showing 4{x} to the power of 2
d A LaTex expression showing 14x
8
A LaTex expression showing \frac{square root of 5{b to the power of 3 } times square root of 45{b to the power of 2 }}{3 over 4 }
Multiply the radical expressions and simplify the answer
a A LaTex expression showing 15bsquare root of b
b A LaTex expression showing 15{b} to the power of 3 square root of b
c A LaTex expression showing 26{b} to the power of 2 square root of b
d A LaTex expression showing 20{b} to the power of 2 square root of b