Radicals

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
Multiply the radical expressions and simplify the answer
A LaTex expression showing \frac{square root of 13{m to the power of 3 } times square root of 325{m to the power of 2 }}{5 over 4 }
a A LaTex expression showing 65{m} to the power of 2 square root of m
b A LaTex expression showing 65{m} to the power of 2
c A LaTex expression showing 41{m} to the power of 2 square root of m
d A LaTex expression showing 52{m} to the power of 2 square root of m
e A LaTex expression showing 41{m} to the power of 2
2
Multiply the radical expressions and simplify the answer
A LaTex expression showing \frac{square root of 7{p to the power of 3 } times square root of 63{p to the power of 2 }}{7 over 4 }
a A LaTex expression showing 21psquare root of p
b A LaTex expression showing 12{p} to the power of 2 square root of p
c A LaTex expression showing 21{p} to the power of 2 square root of p
d A LaTex expression showing 21{p} to the power of 3 square root of p
3
Multiply the radical expressions and simplify the answer
A LaTex expression showing \frac{square root of 208r times square root of 13{r to the power of 2 }}{2 over 5 }
a A LaTex expression showing 52rsquare root of r
b A LaTex expression showing 52{r} to the power of 2
c A LaTex expression showing 130rsquare root of r
d A LaTex expression showing 325rsquare root of r
4
Multiply the radical expressions and simplify the answer
A LaTex expression showing \frac{square root of 3{w to the power of 3 } times square root of 27w}{3 over 2 }
a A LaTex expression showing 27{w} to the power of 2
b A LaTex expression showing {w} to the power of 2
c A LaTex expression showing 6{w} to the power of 2
d A LaTex expression showing 4{w} to the power of 2
e A LaTex expression showing 9{w} to the power of 2
5
Multiply the radical expressions and simplify the answer
A LaTex expression showing \frac{square root of 5{q to the power of 4 } times square root of 80{q to the power of 2 }}{2 over 3 }
a A LaTex expression showing 45{q} to the power of 4
b A LaTex expression showing 20{q} to the power of 4
c A LaTex expression showing 30{q} to the power of 3
d A LaTex expression showing 45{q} to the power of 3
e A LaTex expression showing 20{q} to the power of 3
6
Multiply the radical expressions and simplify the answer
A LaTex expression showing \frac{square root of 18 times square root of 2}{3 over 4 }
a A LaTex expression showing 10
b A LaTex expression showing 30
c A LaTex expression showing 8
d A LaTex expression showing 6
7
Multiply the radical expressions and simplify the answer
A LaTex expression showing \frac{square root of 3 times square root of 48{p to the power of 3 }}{3 over 5 }
a A LaTex expression showing 20psquare root of p
b A LaTex expression showing 12psquare root of p
c A LaTex expression showing 12{p} to the power of 2 square root of p
d A LaTex expression showing 33psquare root of p
e A LaTex expression showing 12{p} to the power of 2
8
Multiply the radical expressions and simplify the answer
A LaTex expression showing \frac{square root of 7{q to the power of 4 } times square root of 28{q to the power of 3 }}{7 over 5 }
a A LaTex expression showing {q} to the power of 3 square root of q
b A LaTex expression showing 28{q} to the power of 3 square root of q
c A LaTex expression showing 14{q} to the power of 3
d A LaTex expression showing 10{q} to the power of 3 square root of q
e A LaTex expression showing 7{q} to the power of 3