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 48 times square root of 75{n to the power of 4 }}{2}
a A LaTex expression showing 15{n} to the power of 2
b A LaTex expression showing 15nsquare root of n
c A LaTex expression showing 30{n} to the power of 2
d A LaTex expression showing 60{n} to the power of 2
e A LaTex expression showing 300{n} to the power of 2
2
Multiply the radical expressions and simplify the answer
A LaTex expression showing \frac{square root of 99{b to the power of 2 } times square root of 44{b to the power of 4 }}{11}
a A LaTex expression showing 66{b} to the power of 3
b A LaTex expression showing 6{b} to the power of 3
c A LaTex expression showing 264{b} to the power of 3
d A LaTex expression showing 66{b} to the power of 2
e A LaTex expression showing 66{b} to the power of 3 square root of b
3
Multiply the radical expressions and simplify the answer
A LaTex expression showing \frac{square root of 18b times square root of 50}{3}
a A LaTex expression showing 10square root of b
b A LaTex expression showing 30square root of b
c A LaTex expression showing square root of b
d A LaTex expression showing 30
4
Multiply the radical expressions and simplify the answer
A LaTex expression showing \frac{square root of 28{b to the power of 3 } times square root of 63{b to the power of 2 }}{3}
a A LaTex expression showing 42{b} to the power of 2 square root of b
b A LaTex expression showing 4{b} to the power of 2 square root of b
c A LaTex expression showing {b} to the power of 2 square root of b
d A LaTex expression showing 14{b} to the power of 2 square root of b
5
Multiply the radical expressions and simplify the answer
A LaTex expression showing \frac{square root of 20 times square root of 45{z to the power of 4 }}{2}
a A LaTex expression showing 30{z} to the power of 2
b A LaTex expression showing 7{z} to the power of 2
c A LaTex expression showing 15{z} to the power of 2
d A LaTex expression showing 30{z} to the power of 3
6
Multiply the radical expressions and simplify the answer
A LaTex expression showing \frac{square root of 99 times square root of 44n}{2}
a A LaTex expression showing 198square root of n
b A LaTex expression showing 66square root of n
c A LaTex expression showing 33square root of n
d A LaTex expression showing 16nsquare root of n
7
Multiply the radical expressions and simplify the answer
A LaTex expression showing \frac{square root of 75{p to the power of 4 } times square root of 27{p to the power of 3 }}{3}
a A LaTex expression showing 45{p} to the power of 2 square root of p
b A LaTex expression showing 5{p} to the power of 3 square root of p
c A LaTex expression showing 45{p} to the power of 3 square root of p
d A LaTex expression showing 15{p} to the power of 3 square root of p
e A LaTex expression showing 180{p} to the power of 3 square root of p
8
Multiply the radical expressions and simplify the answer
A LaTex expression showing \frac{square root of 27x times square root of 48{x to the power of 4 }}{2}
a A LaTex expression showing 18{x} to the power of 2 square root of x
b A LaTex expression showing 36{x} to the power of 3 square root of x
c A LaTex expression showing 36{x} to the power of 2 square root of x
d A LaTex expression showing 9{x} to the power of 3 square root of x
e A LaTex expression showing 9{x} to the power of 2 square root of x