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Radicals - Multiplying Monomials (Values and Variables) (Level 3)

This math topic focuses on multiplying monomials involving radicals, where students practice simplifying expressions that combine both numerical coefficients and variables under the radical sign. Each problem presents a pair of radical expressions to be multiplied, and students need to simplify the product to the most basic form given multiple-choice answers. Skills practiced include multiplying coefficients and exponents and simplifying radicals. This is part of a broader introduction to multiplication with radicals, geared toward enhancing students' algebraic manipulation skills with roots and powers.

Work on practice problems directly here, or download the printable pdf worksheet to practice offline.

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Multiplying Monomials (Values and Variables)

Complete these online problems with 80% or 4 correct answers in a row. Results are immediate.

Multiply the radical expressions and simplify the answer

28n3z3⋅175n3z2\sqrt{28{n}^{3}{z}^{3}} \cdot \sqrt{175{n}^{3}{z}^{2}}

Radicals - Multiplying Monomials (Values and Variables) Worksheet

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Math worksheet on 'Radicals - Multiplying Monomials (Values and Variables) (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 square root of 75r times square root of 27{r to the power of 3 {y} to the power of 2 }
a A LaTex expression showing 45{r} to the power of 3 y
b A LaTex expression showing 45{r} to the power of 2 square root of y
c A LaTex expression showing 45rysquare root of r
d A LaTex expression showing {r} to the power of 2 y
e A LaTex expression showing 45{r} to the power of 2 y
f A LaTex expression showing 45{r} to the power of 2 ysquare root of r
2
Multiply the radical expressions and simplify the answer
A LaTex expression showing square root of 28{n to the power of 3 {z} to the power of 3 } times square root of 175{n to the power of 3 {z} to the power of 2 }
a A LaTex expression showing 70{n} to the power of 2 {z} to the power of 2 square root of nz
b A LaTex expression showing 70{n} to the power of 3 {z} to the power of 3
c A LaTex expression showing 70{n} to the power of 3 {z} to the power of 2 square root of z
d A LaTex expression showing 70{n} to the power of 2 {z} to the power of 2 square root of z
e A LaTex expression showing 70{n} to the power of 3 {z} to the power of 3 square root of z
f A LaTex expression showing 70{n} to the power of 4 {z} to the power of 2 square root of z
3
Multiply the radical expressions and simplify the answer
A LaTex expression showing square root of 75{x to the power of 3 {r} to the power of 2 } times square root of 20x
a A LaTex expression showing 40{x} to the power of 2 rsquare root of 15
b A LaTex expression showing 10{x} to the power of 3 rsquare root of 15
c A LaTex expression showing 10{x} to the power of 2 rsquare root of 15r
d A LaTex expression showing 10{x} to the power of 2 square root of 15r
e A LaTex expression showing 10{x} to the power of 2 rsquare root of 15
f A LaTex expression showing 10{x} to the power of 2 rsquare root of 15x
4
Multiply the radical expressions and simplify the answer
A LaTex expression showing square root of 27{x to the power of 3 {b} to the power of 2 } times square root of 45{b to the power of 2 }
a A LaTex expression showing 9{x} to the power of 2 {b} to the power of 2 square root of 15
b A LaTex expression showing 9x{b} to the power of 2 square root of 15x
c A LaTex expression showing 36x{b} to the power of 2 square root of 15x
d A LaTex expression showing x{b} to the power of 2 square root of x
e A LaTex expression showing 18x{b} to the power of 2 square root of 15x
f A LaTex expression showing 9xbsquare root of 15xb
5
Multiply the radical expressions and simplify the answer
A LaTex expression showing square root of 44{y to the power of 3 {d} to the power of 2 } times square root of 63{y to the power of 3 d}
a A LaTex expression showing 6{y} to the power of 3 dsquare root of 77d
b A LaTex expression showing {y} to the power of 3 dsquare root of d
c A LaTex expression showing 30{y} to the power of 3 dsquare root of 77d
d A LaTex expression showing 6{y} to the power of 3 {d} to the power of 2 square root of 77d
e A LaTex expression showing 12{y} to the power of 3 dsquare root of 77d
f A LaTex expression showing 6{y} to the power of 3 dsquare root of 77
6
Multiply the radical expressions and simplify the answer
A LaTex expression showing square root of 63z times square root of 8{z to the power of 3 }
a A LaTex expression showing 6{z} to the power of 2 square root of 14
b A LaTex expression showing 12{z} to the power of 2 square root of 14
c A LaTex expression showing {z} to the power of 2
d A LaTex expression showing 6{z} to the power of 3 square root of 14
e A LaTex expression showing 6{z} to the power of 2 square root of 14z
f A LaTex expression showing 18{z} to the power of 2 square root of 14
7
Multiply the radical expressions and simplify the answer
A LaTex expression showing square root of 50m{z to the power of 3 } times square root of 75z
a A LaTex expression showing 75{z} to the power of 2 square root of 6m
b A LaTex expression showing 25{z} to the power of 2 square root of 6mz
c A LaTex expression showing 25m{z} to the power of 2 square root of 6m
d A LaTex expression showing 25zsquare root of 6m
e A LaTex expression showing 25{z} to the power of 2 square root of 6m
f A LaTex expression showing 25{z} to the power of 2 square root of 6