Multiplying Monomials with Binomials (Values and Variables) (Level 4)

This math topic focuses on the practice of multiplying radical expressions involving monomials and binomials, coupled with variables and numerical values. Specifically, it covers various intricacies of simplifying radicals that result from multiplication, requiring integration of skills such as combining like terms, handling variable exponents appropriately, and executing arithmetic operations under radical signs. The problems advance through multiple examples to enhance proficiency with radical expressions involving square roots, cube roots, and their higher-order roots across different mathematical operations.

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

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Radicals - Multiplying Monomials with Binomials (Values and Variables) Worksheet

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Math worksheet on 'Radicals - Multiplying Monomials with Binomials (Values and Variables) (Level 4)'. 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 2{x} to the power of 2 square root of 3 times (4xrsquare root of 2x + square root of 3x)
a A LaTex expression showing 8{x} to the power of 4 rsquare root of 6 + 6{x} to the power of 2 square root of x
b A LaTex expression showing 8{x} to the power of 3 rsquare root of 6x + 6{x} to the power of 3
c A LaTex expression showing 8{x} to the power of 5 rsquare root of 6x + 6{x} to the power of 2 square root of x
d A LaTex expression showing 8{x} to the power of 3 rsquare root of 6x + 3{x} to the power of 2 square root of x
e A LaTex expression showing 8{x} to the power of 3 rsquare root of 6x + 6{x} to the power of 2 square root of x
2
Multiply the radical expressions and simplify the answer
A LaTex expression showing (5csquare root of 13y + ycsquare root of 2yc) times 2ysquare root of 3
a A LaTex expression showing 10ycsquare root of 39y + 2{y} to the power of 2 csquare root of 6yc
b A LaTex expression showing 10ycsquare root of 39y + 2{y} to the power of 2 csquare root of 6y
c A LaTex expression showing 10ycsquare root of 39y + 2{y} to the power of 3 csquare root of 6c
d A LaTex expression showing 10ycsquare root of 39y + 2{y} to the power of 2 csquare root of yc
e A LaTex expression showing 10ycsquare root of 39 + 2{y} to the power of 2 csquare root of 6yc
3
Multiply the radical expressions and simplify the answer
A LaTex expression showing (2xsquare root of 5xp + xsquare root of 3p) times 2square root of 7x
a A LaTex expression showing 4{x} to the power of 2 square root of 35p + 2{x} to the power of 2 square root of 21xp
b A LaTex expression showing 4{x} to the power of 2 square root of 35p + 2{x} to the power of -1 square root of 21xp
c A LaTex expression showing 4{x} to the power of 2 square root of 35p + 2xsquare root of 21x{p to the power of -1 }
d A LaTex expression showing 4{x} to the power of 2 square root of 35p + 2xsquare root of 21xp
e A LaTex expression showing 4{x} to the power of 2 square root of 35p + xsquare root of 21xp
4
Multiply the radical expressions and simplify the answer
A LaTex expression showing 4{p} to the power of 2 square root of 2z times ({p} to the power of 2 square root of 11 + 2{z} to the power of 2 psquare root of 3)
a A LaTex expression showing 4{p} to the power of 4 square root of 22z + 8{p} to the power of 3 {z} to the power of 2 square root of 6z
b A LaTex expression showing 4{p} to the power of 4 square root of 22z + 8{p} to the power of 3 {z} to the power of 2 square root of 6
c A LaTex expression showing 4{p} to the power of 4 square root of 22z + 8{p} to the power of 3 {z} to the power of 3 square root of 6z
d A LaTex expression showing {p} to the power of 4 square root of 22z + 8{p} to the power of 3 {z} to the power of 2 square root of 6z
5
Multiply the radical expressions and simplify the answer
A LaTex expression showing 2square root of 13md times (mdsquare root of 3d + 2dsquare root of 13d)
a A LaTex expression showing 2m{d} to the power of 2 square root of 39 + 52{d} to the power of 2 square root of m
b A LaTex expression showing 2m{d} to the power of 2 square root of 39m + 52{d} to the power of 2 square root of m
c A LaTex expression showing 2{m} to the power of -1 {d} to the power of 2 square root of 39m + 52{d} to the power of 2 square root of m
d A LaTex expression showing 2m{d} to the power of 2 square root of 39m + 52{d} to the power of 2 square root of {m to the power of -1 }
e A LaTex expression showing m{d} to the power of 2 square root of 39m + 52{d} to the power of 2 square root of m
6
Multiply the radical expressions and simplify the answer
A LaTex expression showing 2square root of 5x times (5{d} to the power of 2 square root of 5x + dxsquare root of 13x)
a A LaTex expression showing 50{d} to the power of 2 xsquare root of x + 2d{x} to the power of 2 square root of 65
b A LaTex expression showing 50{d} to the power of 2 x + 2d{x} to the power of 2 square root of 65
c A LaTex expression showing 50{d} to the power of 2 x + 2{d} to the power of -1 {x} to the power of 2 square root of 65
d A LaTex expression showing 5{d} to the power of 2 x + 2d{x} to the power of 2 square root of 65
e A LaTex expression showing 50{d} to the power of 2 x + 2{d} to the power of 2 {x} to the power of 2 square root of 65
7
A LaTex expression showing 3{z} to the power of 2 square root of 11n times (5nzsquare root of 2n + nsquare root of 3nz)
Multiply the radical expressions and simplify the answer
a A LaTex expression showing 15{z} to the power of 3 {n} to the power of 3 square root of 22 + 3{z} to the power of 2 {n} to the power of 2 square root of 33z
b A LaTex expression showing 15{z} to the power of 3 {n} to the power of 2 square root of 22 + 3{z} to the power of 2 {n} to the power of 2 square root of 33z
c A LaTex expression showing 15{z} to the power of 3 {n} to the power of 2 square root of 22 + 2{z} to the power of 2 {n} to the power of 2 square root of 33z
d A LaTex expression showing 15{z} to the power of 3 nsquare root of 22n + 3{z} to the power of 2 {n} to the power of 2 square root of 33z