Radicals

Multiplying Monomials (Values and Variables) over Fraction (Level 3)

This math topic focuses on practicing the multiplication of monomial radical expressions that include variables and values, particularly when these expressions are presented as fractions. It allows students to explore the simplification of radical products involving numerical and variable factors. Each question presents various answer options, suggesting a multiple-choice format that reinforces understanding of radical expressions and complex algebraic multiplication. The topic is a deeper dive into multiplying and simplifying radicals, which is part of an introductory curriculum on radical multiplications.

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 44{z to the power of 3 } times square root of 48{q to the power of 3 {z} to the power of 3 }}{2 over 5 }
a A LaTex expression showing 50{z} to the power of 2 qsquare root of 33q
b A LaTex expression showing 20{z} to the power of 3 qsquare root of 33q
c A LaTex expression showing 8{z} to the power of 3 square root of 33q
d A LaTex expression showing 8{z} to the power of 3 qsquare root of 33q
e A LaTex expression showing 32{z} to the power of 3 qsquare root of 33q
2
Multiply the radical expressions and simplify the answer
A LaTex expression showing square root of 175{z to the power of 2 {t} to the power of 3 } times square root of 12t
a A LaTex expression showing 10z{t} to the power of 2 square root of 21
b A LaTex expression showing 10z{t} to the power of 2 square root of 21t
c A LaTex expression showing 10{t} to the power of 2 square root of 21
d A LaTex expression showing 10z{t} to the power of 2
e A LaTex expression showing 20z{t} to the power of 2 square root of 21
3
Multiply the radical expressions and simplify the answer
A LaTex expression showing \frac{square root of 325 times square root of 12m}{2 over 3 }
a A LaTex expression showing 10msquare root of 39m
b A LaTex expression showing 10square root of m
c A LaTex expression showing 15square root of 39m
d A LaTex expression showing 10square root of 39m
4
Multiply the radical expressions and simplify the answer
A LaTex expression showing \frac{square root of 45{w to the power of 4 {y} to the power of 3 } times square root of 63{w to the power of 3 y}}{3 over 5 }
a A LaTex expression showing 9{w} to the power of 2 {y} to the power of 2 square root of 35w
b A LaTex expression showing 9{w} to the power of 3 {y} to the power of 2 square root of 35w
c A LaTex expression showing 25{w} to the power of 3 {y} to the power of 2 square root of 35w
d A LaTex expression showing 15{w} to the power of 3 {y} to the power of 2 square root of 35w
e A LaTex expression showing 25{w} to the power of 3 {y} to the power of 2 square root of 35
5
Multiply the radical expressions and simplify the answer
A LaTex expression showing \frac{square root of 32{n to the power of 2 t} times square root of 28{n to the power of 3 t}}{2 over 5 }
a A LaTex expression showing 8{n} to the power of 2 tsquare root of 14n
b A LaTex expression showing 20{n} to the power of 2 tsquare root of 14n
c A LaTex expression showing 8{n} to the power of 2 tsquare root of 14
d A LaTex expression showing 50{n} to the power of 2 square root of 14n
6
Multiply the radical expressions and simplify the answer
A LaTex expression showing square root of 44{t to the power of 4 n} times square root of 18{t to the power of 4 n}
a A LaTex expression showing 6{t} to the power of 4 nsquare root of 22
b A LaTex expression showing 6{t} to the power of 3 nsquare root of 22
c A LaTex expression showing 6{t} to the power of 3 nsquare root of 22t
d A LaTex expression showing 6{t} to the power of 4 n
7
Multiply the radical expressions and simplify the answer
A LaTex expression showing \frac{square root of 48{m to the power of 3 } times square root of 27}{2 over 5 }
a A LaTex expression showing 90msquare root of m
b A LaTex expression showing 36msquare root of m
c A LaTex expression showing 180msquare root of m
d A LaTex expression showing 225msquare root of m
e A LaTex expression showing 36m
8
Multiply the radical expressions and simplify the answer
A LaTex expression showing \frac{square root of 175{t to the power of 2 {n} to the power of 4 } times square root of 12t{n to the power of 2 }}{2 over 4 }
a A LaTex expression showing 40t{n} to the power of 4 square root of 21t
b A LaTex expression showing 10t{n} to the power of 2 square root of 21tn
c A LaTex expression showing 20t{n} to the power of 3 square root of 21t
d A LaTex expression showing 10{n} to the power of 3 square root of 21t
e A LaTex expression showing 10t{n} to the power of 2 square root of 21t