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Radicals - 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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Multiplying Monomials with Binomials (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

2n2⋅(5b3b−b22n)2n\sqrt{2} \cdot (5b\sqrt{3b} - {b}^{2}\sqrt{2n})

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 (5zsquare root of 2xz - zsquare root of 11) times 5xsquare root of 2x
a A LaTex expression showing 50{x} to the power of 2 zsquare root of z - 5xzsquare root of 22{x to the power of -1 }
b A LaTex expression showing 50{x} to the power of 2 zsquare root of z - 5xzsquare root of 22x
c A LaTex expression showing 50{x} to the power of 2 {z} to the power of -1 square root of z - 5xzsquare root of 22x
d A LaTex expression showing 50{x} to the power of 3 zsquare root of z - 5xzsquare root of 22x
e A LaTex expression showing 50{x} to the power of 2 zsquare root of z - 5xzsquare root of x
f A LaTex expression showing 50{x} to the power of 2 zsquare root of z - 5{x} to the power of 2 zsquare root of 22
2
Multiply the radical expressions and simplify the answer
A LaTex expression showing (2m3-th root of 3 - m3-th root of 3) times 2pm3-th root of 3p
a A LaTex expression showing 2p{m} to the power of 2 3-th root of 9p
b A LaTex expression showing 4p{m} to the power of 2 3-th root of 9p - 2p{m} to the power of 2 3-th root of 9{p to the power of 2 }
c A LaTex expression showing 4p{m} to the power of 2 3-th root of 9p - 2{p} to the power of 2 {m} to the power of 2 3-th root of 9
d A LaTex expression showing 4p{m} to the power of 4 3-th root of 9p - 2p{m} to the power of 2 3-th root of 9p
e A LaTex expression showing 4p{m} to the power of 2 3-th root of 9p - 2p{m} to the power of 2 3-th root of 9
f A LaTex expression showing 4p{m} to the power of 2 3-th root of 9 - 2p{m} to the power of 2 3-th root of 9p
3
A LaTex expression showing 5{m} to the power of 2 zsquare root of 2z times (mzsquare root of 11m + 4m{z} to the power of 2 square root of 2)
Multiply the radical expressions and simplify the answer
a A LaTex expression showing 5{m} to the power of 3 {z} to the power of 2 square root of 22zm + 40{m} to the power of 3 {z} to the power of 3 square root of z
b A LaTex expression showing 5{m} to the power of 3 {z} to the power of 2 square root of zm + 40{m} to the power of 3 {z} to the power of 3 square root of z
c A LaTex expression showing 5{m} to the power of 3 {z} to the power of 2 square root of 22zm + 40{m} to the power of 3 {z} to the power of 4
d A LaTex expression showing 5{m} to the power of 3 {z} to the power of 2 square root of 22zm + 40{m} to the power of 3 {z} to the power of 3 square root of {z to the power of -1 }
e A LaTex expression showing 5{m} to the power of 3 {z} to the power of 2 square root of 2zm + 40{m} to the power of 3 {z} to the power of 3 square root of z
f A LaTex expression showing 5{m} to the power of 3 {z} to the power of 2 square root of 22zm + 40{m} to the power of 3 {z} to the power of 3
4
Multiply the radical expressions and simplify the answer
A LaTex expression showing 2nsquare root of 2 times (5bsquare root of 3b - {b} to the power of 2 square root of 2n)
a A LaTex expression showing 10n{b} to the power of 3 square root of 6b - 4n{b} to the power of 2 square root of n
b A LaTex expression showing 10nbsquare root of 6b - 2n{b} to the power of 2 square root of 2n
c A LaTex expression showing 10nbsquare root of 6b - 4{n} to the power of 2 {b} to the power of 2
d A LaTex expression showing 10nbsquare root of 6b - 4n{b} to the power of 2 square root of n
e A LaTex expression showing 10nbsquare root of 6b - 4n{b} to the power of 2
f A LaTex expression showing 10n{b} to the power of 2 square root of 6b - 4n{b} to the power of 2 square root of n
5
Multiply the radical expressions and simplify the answer
A LaTex expression showing 5{z} to the power of 2 square root of 11 times (square root of 13 + 2square root of 3z)
a A LaTex expression showing 5{z} to the power of 2 + 10{z} to the power of 2 square root of 33z
b A LaTex expression showing 5{z} to the power of 2 square root of 143 + 10zsquare root of 33z
c A LaTex expression showing 5{z} to the power of 2 square root of 143 + 10{z} to the power of 2 square root of 33z
d A LaTex expression showing 5{z} to the power of 2 square root of 143 + 10{z} to the power of 3 square root of 33
e A LaTex expression showing 5{z} to the power of 4 square root of 143 + 10{z} to the power of 2 square root of 33z
f A LaTex expression showing 5{z} to the power of 2 square root of 143 + 10square root of 33z
6
Multiply the radical expressions and simplify the answer
A LaTex expression showing 23-th root of 2xd times (x3-th root of 7d + 33-th root of 11{x to the power of 2 })
a A LaTex expression showing 2x3-th root of 14x{d to the power of 2 } + x3-th root of 22d
b A LaTex expression showing 3x3-th root of 14x{d to the power of 2 } + 6x3-th root of 22d
c A LaTex expression showing 2{x} to the power of 3 3-th root of 14x{d to the power of 2 } + 6x3-th root of 22d
d A LaTex expression showing 2x3-th root of 14x{d to the power of 2 } + 6x3-th root of 22d
e A LaTex expression showing 2x3-th root of x{d to the power of 2 } + 6x3-th root of 22d
f A LaTex expression showing 2{x} to the power of 2 3-th root of 14{d to the power of 2 } + 6x3-th root of 22d
7
Multiply the radical expressions and simplify the answer
A LaTex expression showing 2c3-th root of 3cn times (cn3-th root of 5cn + 3c3-th root of 7)
a A LaTex expression showing 2{c} to the power of 2 n3-th root of 15{c to the power of 2 {n} to the power of 2 } + 6{c} to the power of 3 3-th root of 21cn
b A LaTex expression showing 2{c} to the power of 3 n3-th root of 15c{n to the power of 2 } + 6{c} to the power of 2 3-th root of 21cn
c A LaTex expression showing {c} to the power of 2 n3-th root of 15{c to the power of 2 {n} to the power of 2 } + 6{c} to the power of 2 3-th root of 21cn
d A LaTex expression showing 2{c} to the power of 2 n3-th root of 15{c to the power of 2 {n} to the power of 2 } + 6c3-th root of 21cn
e A LaTex expression showing 2{c} to the power of 2 n3-th root of 15{c to the power of 2 {n} to the power of 2 } + 6{c} to the power of 2 3-th root of 3cn
f A LaTex expression showing 2{c} to the power of 2 n3-th root of 15{c to the power of 2 {n} to the power of 2 } + 6{c} to the power of 2 3-th root of 21cn