Radicals

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.

more

Radicals - Multiplying Monomials (Values and Variables) over Integer Worksheet

Mobius Math Academy logo
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 50{t to the power of 3 q} times square root of 45{t to the power of 3 q}}{3}
a A LaTex expression showing 60{t} to the power of 3 qsquare root of 10
b A LaTex expression showing 5{t} to the power of 3 qsquare root of 10
c A LaTex expression showing 45{t} to the power of 3 qsquare root of 10
d A LaTex expression showing {t} to the power of 3 square root of 10
e A LaTex expression showing 15{t} to the power of 3 square root of 10q
2
Multiply the radical expressions and simplify the answer
A LaTex expression showing \frac{square root of 28w{n to the power of 2 } times square root of 20wn}{2}
a A LaTex expression showing nsquare root of 35n
b A LaTex expression showing 2wnsquare root of 35n
c A LaTex expression showing w{n} to the power of 2 square root of 35
d A LaTex expression showing 4wnsquare root of 35n
e A LaTex expression showing 16wnsquare root of 35n
3
Multiply the radical expressions and simplify the answer
A LaTex expression showing \frac{square root of 28{w to the power of 4 n} times square root of 12{w to the power of 3 {n} to the power of 3 }}{2}
a A LaTex expression showing 2{w} to the power of 3 {n} to the power of 2 square root of 21w
b A LaTex expression showing 4{w} to the power of 3 {n} to the power of 3 square root of 21w
c A LaTex expression showing {w} to the power of 3 {n} to the power of 2 square root of 21w
d A LaTex expression showing 4{w} to the power of 3 {n} to the power of 2 square root of 21
e A LaTex expression showing {w} to the power of 3 {n} to the power of 2 square root of 21
4
Multiply the radical expressions and simplify the answer
A LaTex expression showing \frac{square root of 20{p to the power of 3 } times square root of 18{x to the power of 2 p}}{3}
a A LaTex expression showing 0{p} to the power of 2 x
b A LaTex expression showing 6{p} to the power of 2 x
c A LaTex expression showing 0{p} to the power of 2 xsquare root of 10
d A LaTex expression showing {p} to the power of 2 x
e A LaTex expression showing 2{p} to the power of 2 xsquare root of 10
5
Multiply the radical expressions and simplify the answer
A LaTex expression showing \frac{square root of 50n{t to the power of 4 } times square root of 63{n to the power of 2 t}}{5}
a A LaTex expression showing 3n{t} to the power of 2 square root of 14nt
b A LaTex expression showing 15ntsquare root of 14nt
c A LaTex expression showing 0{n} to the power of 2 {t} to the power of 2 square root of 14t
d A LaTex expression showing 0n{t} to the power of 2 square root of 14nt
e A LaTex expression showing 45n{t} to the power of 2 square root of 14nt
6
Multiply the radical expressions and simplify the answer
A LaTex expression showing \frac{square root of 50w{q to the power of 2 } times square root of 12w{q to the power of 3 }}{2}
a A LaTex expression showing 2w{q} to the power of 3 square root of 6q
b A LaTex expression showing 5w{q} to the power of 2 square root of 6q
c A LaTex expression showing 10{q} to the power of 2 square root of 6wq
d A LaTex expression showing 2{q} to the power of 2 square root of 6q
e A LaTex expression showing 2w{q} to the power of 3 square root of 6
7
Multiply the radical expressions and simplify the answer
A LaTex expression showing \frac{square root of 112{m to the power of 3 } times square root of 8y{m to the power of 4 }}{2}
a A LaTex expression showing 8{m} to the power of 3 square root of 14m{y to the power of -1 }
b A LaTex expression showing 4{m} to the power of 3 square root of 14my
c A LaTex expression showing 8{m} to the power of 3 square root of 14my
d A LaTex expression showing 16{m} to the power of 3 square root of 14my
e A LaTex expression showing 8{m} to the power of 4 square root of 14y
8
Multiply the radical expressions and simplify the answer
A LaTex expression showing \frac{square root of 44n{z to the power of 2 } times square root of 18{z to the power of 3 }}{3}
a A LaTex expression showing 6zsquare root of 22nz
b A LaTex expression showing 0{z} to the power of 2 square root of nz
c A LaTex expression showing 2{z} to the power of 2 square root of 22nz
d A LaTex expression showing 6{z} to the power of 3 square root of 22nz
e A LaTex expression showing 6{z} to the power of 3 square root of 22n