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.

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

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Math worksheet on 'Radicals - Multiplying Monomials (Values and Variables) over Integer (Level 3)'. Part of a broader unit on 'Radicals - Multiplication Intro' Learn online: app.mobius.academy/math/units/radicals_multiplication_intro/
1
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 4{c} to the power of 2 nsquare root of 14c
b A LaTex expression showing 16{c} to the power of 2 square root of 14cn
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 16{c} to the power of 2 square root of 14n
e A LaTex expression showing 8{c} to the power of 2 square root of 14cn
2
Multiply the radical expressions and simplify the answer
A LaTex expression showing \frac{square root of 18{r to the power of 3 } times square root of 50{m to the power of 3 {r} to the power of 3 }}{2}
a A LaTex expression showing 7{r} to the power of 3 msquare root of m
b A LaTex expression showing 30{r} to the power of 3 msquare root of rm
c A LaTex expression showing 120{r} to the power of 3 msquare root of m
d A LaTex expression showing 15{r} to the power of 3 msquare root of m
3
Multiply the radical expressions and simplify the answer
A LaTex expression showing \frac{square root of 99{d to the power of 3 {c} to the power of 2 } times square root of 48{d to the power of 4 {c} to the power of 2 }}{2}
a A LaTex expression showing 12{d} to the power of 3 csquare root of 33dc
b A LaTex expression showing 6{d} to the power of 3 {c} to the power of 2 square root of 33d
c A LaTex expression showing 3{d} to the power of 3 {c} to the power of 2 square root of 33
d A LaTex expression showing 12{d} to the power of 3 {c} to the power of 2 square root of d
e A LaTex expression showing 3{d} to the power of 3 {c} to the power of 2 square root of d
4
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 2{b} to the power of 3 {p} to the power of 4 square root of 10
b A LaTex expression showing {b} to the power of 3 {p} to the power of 4 square root of 10p
c A LaTex expression showing 4{b} to the power of 3 {p} to the power of 3 square root of 10
d A LaTex expression showing 4{b} to the power of 3 {p} to the power of 4
e A LaTex expression showing 4{b} to the power of 3 {p} to the power of 4 square root of 10
5
Multiply the radical expressions and simplify the answer
A LaTex expression showing \frac{square root of 45{z to the power of 3 } times square root of 80{z to the power of 4 {x} to the power of 3 }}{2}
a A LaTex expression showing 60{z} to the power of 4 xsquare root of zx
b A LaTex expression showing 15{z} to the power of 4 xsquare root of zx
c A LaTex expression showing 15{z} to the power of 3 xsquare root of zx
d A LaTex expression showing 60{z} to the power of 3 square root of zx
e A LaTex expression showing 30{z} to the power of 3 xsquare root of zx
6
Multiply the radical expressions and simplify the answer
A LaTex expression showing \frac{square root of 50m times square root of 12m{y to the power of 2 }}{5}
a A LaTex expression showing 10mysquare root of 6y
b A LaTex expression showing 0my
c A LaTex expression showing 2mysquare root of 6
d A LaTex expression showing 10mysquare root of 6m
e A LaTex expression showing 10ysquare root of 6m
7
Multiply the radical expressions and simplify the answer
A LaTex expression showing \frac{square root of 20{x to the power of 2 {r} to the power of 4 } times square root of 44{x to the power of 2 r}}{2}
a A LaTex expression showing 2{x} to the power of 2 {r} to the power of 2 square root of 55r
b A LaTex expression showing 4{x} to the power of 2 {r} to the power of 2 square root of 55r
c A LaTex expression showing {x} to the power of 2 {r} to the power of 2 square root of 55r
d A LaTex expression showing 4{x} to the power of 2 {r} to the power of 2 square root of 55xr
e A LaTex expression showing 4{x} to the power of 2 {r} to the power of 3 square root of 55r