HomePricing
Sign InJoin

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.

View Unit

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

45nx4â‹…44n3x3\sqrt{45n{x}^{4}} \cdot \sqrt{44{n}^{3}{x}^{3}}

Radicals - Multiplying Monomials (Values and Variables) Worksheet

Mobius Math Club logo
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 12{b to the power of 3 {d} to the power of 2 } times square root of 27{b to the power of 3 {d} to the power of 2 }
a A LaTex expression showing {b} to the power of 3 {d} to the power of 2
b A LaTex expression showing 18{b} to the power of 3 {d} to the power of 2
c A LaTex expression showing 18{b} to the power of 3 d
d A LaTex expression showing 54{b} to the power of 3 {d} to the power of 2
e A LaTex expression showing 18{b} to the power of 2 {d} to the power of 2 square root of b
f A LaTex expression showing 18{b} to the power of 2 {d} to the power of 2
2
Multiply the radical expressions and simplify the answer
A LaTex expression showing square root of 45n{x to the power of 4 } times square root of 44{n to the power of 3 {x} to the power of 3 }
a A LaTex expression showing 6{n} to the power of 2 {x} to the power of 3 square root of 55
b A LaTex expression showing 6{n} to the power of 2 {x} to the power of 4 square root of 55
c A LaTex expression showing 6{n} to the power of 2 {x} to the power of 3 square root of 55nx
d A LaTex expression showing 6{n} to the power of 2 {x} to the power of 4 square root of 55x
e A LaTex expression showing 24{n} to the power of 2 {x} to the power of 3 square root of 55x
f A LaTex expression showing 6{n} to the power of 2 {x} to the power of 3 square root of 55x
3
Multiply the radical expressions and simplify the answer
A LaTex expression showing square root of 80{p to the power of 3 {x} to the power of 2 } times square root of 52{x to the power of 2 }
a A LaTex expression showing p{x} to the power of 2 square root of p
b A LaTex expression showing 8p{x} to the power of 2 square root of 65
c A LaTex expression showing 8p{x} to the power of 3 square root of 65p
d A LaTex expression showing 8pxsquare root of 65p
e A LaTex expression showing 8p{x} to the power of 2 square root of 65px
f A LaTex expression showing 8p{x} to the power of 2 square root of 65p
4
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 6{y} to the power of 3 {d} to the power of 2 square root of 77d
c A LaTex expression showing {y} to the power of 3 dsquare root of d
d A LaTex expression showing 12{y} to the power of 3 dsquare root of 77d
e A LaTex expression showing 6{y} to the power of 3 dsquare root of 77
f A LaTex expression showing 30{y} to the power of 3 dsquare root of 77d
5
Multiply the radical expressions and simplify the answer
A LaTex expression showing square root of 28{x to the power of 3 } times square root of 52{y to the power of 2 }
a A LaTex expression showing 4xysquare root of 91x
b A LaTex expression showing 4{x} to the power of 2 ysquare root of 91x
c A LaTex expression showing 4x{y} to the power of 2 square root of 91x
d A LaTex expression showing 4ysquare root of 91x
e A LaTex expression showing 4xsquare root of 91x
f A LaTex expression showing 12xysquare root of 91x
6
Multiply the radical expressions and simplify the answer
A LaTex expression showing square root of 28{p to the power of 3 } times square root of 32{y to the power of 3 {p} to the power of 3 }
a A LaTex expression showing 8{p} to the power of 3 {y} to the power of 2 square root of 14y
b A LaTex expression showing 8{p} to the power of 3 ysquare root of 14y
c A LaTex expression showing 16{p} to the power of 3 ysquare root of 14y
d A LaTex expression showing 8{p} to the power of 3 ysquare root of 14py
e A LaTex expression showing 8{p} to the power of 2 ysquare root of 14y
f A LaTex expression showing {p} to the power of 3 ysquare root of y
7
Multiply the radical expressions and simplify the answer
A LaTex expression showing square root of 52{b to the power of 2 } times square root of 18{b to the power of 3 {r} to the power of 4 }
a A LaTex expression showing 6{b} to the power of 2 rsquare root of 26b
b A LaTex expression showing 6{b} to the power of 2 {r} to the power of 2 square root of 26b
c A LaTex expression showing 6{b} to the power of 3 {r} to the power of 2 square root of 26
d A LaTex expression showing 6{b} to the power of 2 {r} to the power of 3 square root of 26b
e A LaTex expression showing 30{b} to the power of 2 {r} to the power of 2 square root of 26b
f A LaTex expression showing 6b{r} to the power of 2 square root of 26b