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

This math topic focuses on multiplying monomial radical expressions with integer coefficients. It includes simplifying the product to its lowest terms, involving both values and variables. The expressions have a complexity involving square roots of products with varying degrees of variables. The exercises provide practice in handling radicals where participants must identify the correct simplified form from multiple choices, enhancing their skills in radical operations and algebraic simplification.

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 80{d to the power of 4 {m} to the power of 3 } times square root of 45{m to the power of 2 }}{3}
a A LaTex expression showing 20{d} to the power of 2 {m} to the power of 2 square root of m
b A LaTex expression showing {d} to the power of 2 {m} to the power of 2 square root of m
c A LaTex expression showing 60{d} to the power of 2 msquare root of m
d A LaTex expression showing 60{d} to the power of 2 {m} to the power of 2 square root of m
e A LaTex expression showing 60d{m} to the power of 2 square root of m
2
Multiply the radical expressions and simplify the answer
A LaTex expression showing \frac{square root of 112{c to the power of 4 } times square root of 32cn}{2}
a A LaTex expression showing 8{c} to the power of 2 square root of 14cn
b A LaTex expression showing 16{c} to the power of 2 square root of 14n
c A LaTex expression showing 4{c} to the power of 2 square root of 14c{n to the power of -1 }
d A LaTex expression showing 4{c} to the power of 2 nsquare root of 14c
e A LaTex expression showing 16{c} to the power of 2 square root of 14cn
3
Multiply the radical expressions and simplify the answer
A LaTex expression showing \frac{square root of 8y times square root of 208{y to the power of 2 }}{2}
a A LaTex expression showing 8square root of 26y
b A LaTex expression showing 16ysquare root of 26y
c A LaTex expression showing 4ysquare root of 26y
d A LaTex expression showing 2ysquare root of 26
e A LaTex expression showing 8{y} to the power of 2 square root of 26y
4
Multiply the radical expressions and simplify the answer
A LaTex expression showing \frac{square root of 18{z to the power of 2 {b} to the power of 3 } times square root of 12b}{2}
a A LaTex expression showing 6{b} to the power of 2 square root of 6z
b A LaTex expression showing z{b} to the power of 2 square root of 6
c A LaTex expression showing 6z{b} to the power of 2 square root of 6
d A LaTex expression showing 3z{b} to the power of 2 square root of 6
e A LaTex expression showing 6zbsquare root of 6b
5
Multiply the radical expressions and simplify the answer
A LaTex expression showing \frac{square root of 63{z to the power of 2 d} times square root of 50zd}{3}
a A LaTex expression showing {z} to the power of 2 dsquare root of 14z
b A LaTex expression showing zdsquare root of 14zd
c A LaTex expression showing 15zdsquare root of 14z
d A LaTex expression showing 5zdsquare root of 14z
e A LaTex expression showing 15{z} to the power of 2 dsquare root of 14
6
Multiply the radical expressions and simplify the answer
A LaTex expression showing \frac{square root of 325{z to the power of 3 } times square root of 8{z to the power of 2 {n} to the power of 2 }}{5}
a A LaTex expression showing 0{z} to the power of 3 nsquare root of 26
b A LaTex expression showing 2{z} to the power of 2 nsquare root of 26z
c A LaTex expression showing 0{z} to the power of 2 square root of 26zn
d A LaTex expression showing 0{z} to the power of 2 nsquare root of 26zn
e A LaTex expression showing 10{z} to the power of 2 nsquare root of 26zn
7
Multiply the radical expressions and simplify the answer
A LaTex expression showing \frac{square root of 8{z to the power of 3 {p} to the power of 3 } times square root of 18{z to the power of 3 }}{2}
a A LaTex expression showing 3{z} to the power of 3 psquare root of p
b A LaTex expression showing 12{z} to the power of 3 psquare root of p
c A LaTex expression showing 6{z} to the power of 3 psquare root of p
d A LaTex expression showing 12{z} to the power of 3 psquare root of zp
8
Multiply the radical expressions and simplify the answer
A LaTex expression showing \frac{square root of 20{b to the power of 2 {p} to the power of 4 } times square root of 8{b to the power of 4 {p} to the power of 4 }}{2}
a A LaTex expression showing 4{b} to the power of 3 {p} to the power of 4 square root of 10
b A LaTex expression showing 4{b} to the power of 3 {p} to the power of 3 square root of 10
c A LaTex expression showing 2{b} to the power of 3 {p} to the power of 4 square root of 10
d A LaTex expression showing {b} to the power of 3 {p} to the power of 4 square root of 10p
e A LaTex expression showing 4{b} to the power of 3 {p} to the power of 4