Radicals

Multiplying Monomials (Values and Variables) over Integer (Level 2)

This math topic focuses on multiplying and simplifying radical expressions involving monomials with variables and integers. Each problem requires multiplying two radical terms, each with variable expressions raised to different powers, and then simplifying the result. Most problems are structured with multiple-choice answers to select the correctly simplified form of the expression. The skills practiced are essential for algebraic manipulation involving roots and powers, suitable for students learning introductory radical operations.

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 Integer Worksheet

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Radicals - Multiplying Monomials (Values and Variables) over Integer
1
Multiply the radical expressions and simplify the answer
A LaTex expression showing \frac{square root of 12{t to the power of 4 } times square root of 27t}{3}
a A LaTex expression showing 18{t} to the power of 3
b A LaTex expression showing {t} to the power of 2 square root of t
c A LaTex expression showing 6{t} to the power of 2 square root of t
d A LaTex expression showing 18{t} to the power of 2
e A LaTex expression showing 18{t} to the power of 2 square root of t
2
Multiply the radical expressions and simplify the answer
A LaTex expression showing \frac{square root of 80{q to the power of 2 } times square root of 20}{5}
a A LaTex expression showing 40
b A LaTex expression showing 40{q} to the power of 2
c A LaTex expression showing q
d A LaTex expression showing 40q
e A LaTex expression showing 8q
3
Multiply the radical expressions and simplify the answer
A LaTex expression showing \frac{square root of 32{t to the power of 4 } times square root of 18{t to the power of 2 }}{3}
a A LaTex expression showing 24{t} to the power of 3 square root of t
b A LaTex expression showing 24{t} to the power of 2 square root of t
c A LaTex expression showing 8{t} to the power of 3
d A LaTex expression showing 24{t} to the power of 2
e A LaTex expression showing 24{t} to the power of 3
4
Multiply the radical expressions and simplify the answer
A LaTex expression showing \frac{square root of 18q times square root of 32}{3}
a A LaTex expression showing 24
b A LaTex expression showing 72square root of q
c A LaTex expression showing 8square root of q
d A LaTex expression showing 24q
e A LaTex expression showing 2
5
Multiply the radical expressions and simplify the answer
A LaTex expression showing \frac{square root of 8{y to the power of 3 } times square root of 32}{2}
a A LaTex expression showing 4square root of y
b A LaTex expression showing 4ysquare root of y
c A LaTex expression showing 16{y} to the power of 2 square root of y
d A LaTex expression showing 8ysquare root of y
6
Multiply the radical expressions and simplify the answer
A LaTex expression showing \frac{square root of 75{m to the power of 4 } times square root of 27{m to the power of 2 }}{5}
a A LaTex expression showing 180{m} to the power of 3
b A LaTex expression showing 45{m} to the power of 4
c A LaTex expression showing 9{m} to the power of 3
d A LaTex expression showing 45{m} to the power of 2 square root of m
7
Multiply the radical expressions and simplify the answer
A LaTex expression showing \frac{square root of 20 times square root of 80}{2}
a A LaTex expression showing 10
b A LaTex expression showing 120
c A LaTex expression showing 20
d A LaTex expression showing 40
8
Multiply the radical expressions and simplify the answer
A LaTex expression showing \frac{square root of 75{x to the power of 2 } times square root of 12{x to the power of 2 }}{3}
a A LaTex expression showing 10{x} to the power of 2
b A LaTex expression showing 30{x} to the power of 2 square root of x
c A LaTex expression showing 3{x} to the power of 2 square root of x
d A LaTex expression showing 150{x} to the power of 2
e A LaTex expression showing 30{x} to the power of 2