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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

3b3x3â‹…(22b23+x5b23)3b\sqrt[3]{3x} \cdot (2\sqrt[3]{2{b}^{2}} + x\sqrt[3]{5{b}^{2}})

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
A LaTex expression showing 2y3-th root of 11y{x to the power of 2 } times (3-th root of 13y{x to the power of 2 } + 2x3-th root of 5{y to the power of 2 })
Multiply the radical expressions and simplify the answer
a A LaTex expression showing 2yx3-th root of 143{y to the power of 2 x} + 4{y} to the power of 2 x3-th root of 55y{x to the power of 2 }
b A LaTex expression showing 2{y} to the power of 3 x3-th root of 143{y to the power of 2 x} + 4{y} to the power of 2 x3-th root of 55{x to the power of 2 }
c A LaTex expression showing yx3-th root of 143{y to the power of 2 x} + 4{y} to the power of 2 x3-th root of 55{x to the power of 2 }
d A LaTex expression showing 2yx3-th root of 143{y to the power of 2 x} + 4{y} to the power of 2 x3-th root of 55{x to the power of 2 }
e A LaTex expression showing 2yx3-th root of 143{y to the power of 2 x} + 4{y} to the power of 2 {x} to the power of -1 3-th root of 55{x to the power of 2 }
f A LaTex expression showing 2x3-th root of 143{y to the power of 2 x} + 4{y} to the power of 2 x3-th root of 55{x to the power of 2 }
2
A LaTex expression showing 3mbsquare root of 7b times (2{m} to the power of 2 bsquare root of 13 + {m} to the power of 2 {b} to the power of 2 square root of 5)
Multiply the radical expressions and simplify the answer
a A LaTex expression showing 6{m} to the power of 3 {b} to the power of 2 square root of 91b + 3{m} to the power of 2 {b} to the power of 3 square root of 35b
b A LaTex expression showing 6{m} to the power of 5 {b} to the power of 2 square root of 91b + 3{m} to the power of 3 {b} to the power of 3 square root of 35b
c A LaTex expression showing 6{m} to the power of 3 {b} to the power of 3 square root of 91 + 3{m} to the power of 3 {b} to the power of 3 square root of 35b
d A LaTex expression showing 4{m} to the power of 3 {b} to the power of 2 square root of 91b + 3{m} to the power of 3 {b} to the power of 3 square root of 35b
e A LaTex expression showing 6{m} to the power of 3 {b} to the power of 2 square root of 91 + 3{m} to the power of 3 {b} to the power of 3 square root of 35b
f A LaTex expression showing 6{m} to the power of 3 {b} to the power of 2 square root of 91b + 3{m} to the power of 3 {b} to the power of 3 square root of 35b
3
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 9 - 2p{m} to the power of 2 3-th root of 9p
c 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
d 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
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 9p - 2p{m} to the power of 2 3-th root of 9{p to the power of 2 }
4
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 to the power of -1 }
b 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
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 3 square root of z
d 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
e 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
f 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
5
Multiply the radical expressions and simplify the answer
A LaTex expression showing (23-th root of 7d + 3-th root of 3p{d to the power of 2 }) times 23-th root of 7d
a A LaTex expression showing 43-th root of 49{d to the power of 2 } + 2d3-th root of 21{d to the power of 2 p}
b A LaTex expression showing 43-th root of 49{d to the power of 2 } + 3d3-th root of 21p
c A LaTex expression showing 43-th root of 49{d to the power of 2 } + 2d3-th root of 21p
d A LaTex expression showing 43-th root of {d to the power of 2 } + 2d3-th root of 21p
e A LaTex expression showing 43-th root of 49{d to the power of 2 } + d3-th root of 21p
f A LaTex expression showing 43-th root of 49{d to the power of 2 } + 2d3-th root of p
6
Multiply the radical expressions and simplify the answer
A LaTex expression showing (pysquare root of 2 + 3{y} to the power of 2 square root of 2) times 2pysquare root of 7py
a A LaTex expression showing 4{p} to the power of 2 {y} to the power of 2 square root of 14py + 6p{y} to the power of 3 square root of 14py
b A LaTex expression showing 2{p} to the power of 2 {y} to the power of 2 square root of 14py + 6p{y} to the power of 3 square root of 14p
c A LaTex expression showing 2{p} to the power of 2 {y} to the power of 3 square root of 14py + 6p{y} to the power of 3 square root of 14py
d A LaTex expression showing 2{p} to the power of 2 {y} to the power of 2 square root of 14py + 6p{y} to the power of 3 square root of 14py
e A LaTex expression showing 2{p} to the power of 2 {y} to the power of 2 square root of 14y + 6p{y} to the power of 3 square root of 14py
f A LaTex expression showing 2{p} to the power of 4 {y} to the power of 2 square root of 14py + 6p{y} to the power of 3 square root of 14py
7
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 square root of 143 + 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 + 10{z} to the power of 3 square root of 33
c A LaTex expression showing 5{z} to the power of 2 square root of 143 + 10square root of 33z
d A LaTex expression showing 5{z} to the power of 2 square root of 143 + 10zsquare root of 33z
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 + 10{z} to the power of 2 square root of 33z