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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Radicals - Multiplying Monomials with Binomials (Values and Variables)
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 2 square root of x
c 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
d A LaTex expression showing 8{x} to the power of 3 rsquare root of 6x + 6{x} to the power of 3
e 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
2
Multiply the radical expressions and simplify the answer
A LaTex expression showing 23-th root of 5{c to the power of 2 {n} to the power of 2 } times (33-th root of 2n - c3-th root of 13)
a A LaTex expression showing 6n3-th root of 10 - 2c3-th root of 65{c to the power of 2 {n} to the power of 2 }
b A LaTex expression showing 6n3-th root of 10{c to the power of 2 } - 2c3-th root of 65{c to the power of 2 {n} to the power of 2 }
c A LaTex expression showing 6n3-th root of 10{c to the power of 2 } - 2cn3-th root of 65{c to the power of 2 n}
d A LaTex expression showing 6n3-th root of 10{c to the power of 2 } - 2{c} to the power of 2 3-th root of 65{n to the power of 2 }
3
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 6y
b A LaTex expression showing 10ycsquare root of 39 + 2{y} to the power of 2 csquare root of 6yc
c A LaTex expression showing 10ycsquare root of 39y + 2{y} to the power of 2 csquare root of 6yc
d A LaTex expression showing 10ycsquare root of 39y + 2{y} to the power of 3 csquare root of 6c
e A LaTex expression showing 10ycsquare root of 39y + 2{y} to the power of 2 csquare root of yc
4
Multiply the radical expressions and simplify the answer
A LaTex expression showing (3xsquare root of 2b - xbsquare root of 2xb) times 2{x} to the power of 2 {b} to the power of 2 square root of 7
a A LaTex expression showing 6{x} to the power of 3 {b} to the power of 2 square root of 14b - 2{x} to the power of 3 {b} to the power of 3 square root of 14xb
b A LaTex expression showing 6{x} to the power of 3 {b} to the power of 3 square root of 14b - 2{x} to the power of 3 {b} to the power of 3 square root of 14xb
c A LaTex expression showing 6{x} to the power of 3 {b} to the power of 2 square root of 14b - 2{x} to the power of 3 {b} to the power of 3 square root of 14b
d A LaTex expression showing 6{x} to the power of 3 {b} to the power of 2 square root of 14b - 2{x} to the power of 3 {b} to the power of 4 square root of 14x
5
Multiply the radical expressions and simplify the answer
A LaTex expression showing (n{d} to the power of 2 square root of 7 - 2n{d} to the power of 2 square root of 2) times 2nsquare root of 13n
a A LaTex expression showing 4{n} to the power of 2 {d} to the power of 2 square root of 91n - 4{n} to the power of 2 {d} to the power of 2 square root of 26n
b A LaTex expression showing 2{n} to the power of 2 {d} to the power of 2 square root of 91n - 4{n} to the power of 2 {d} to the power of 2 square root of 26n
c A LaTex expression showing 2{n} to the power of 2 {d} to the power of 3 square root of 91n - 4{n} to the power of 2 {d} to the power of 2 square root of 26n
d A LaTex expression showing 2{n} to the power of 2 {d} to the power of 2 square root of 91n - 4{n} to the power of 3 {d} to the power of 2 square root of 26n
e A LaTex expression showing 2{n} to the power of 2 {d} to the power of 2 square root of 91n - 4n{d} to the power of 2 square root of 26n
6
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 3 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 2 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
7
Multiply the radical expressions and simplify the answer
A LaTex expression showing 5dsquare root of 7dy times ({d} to the power of 2 {y} to the power of 2 square root of 2 - 2square root of 2y)
a A LaTex expression showing 5{d} to the power of 3 {y} to the power of 2 square root of 14dy - 10{d} to the power of 3 ysquare root of 14d
b A LaTex expression showing 5{d} to the power of 3 {y} to the power of 3 square root of 14dy - 10dysquare root of 14d
c A LaTex expression showing 5{d} to the power of 3 {y} to the power of 2 square root of 14dy - 10dysquare root of 14d
d A LaTex expression showing 5{d} to the power of 3 {y} to the power of 2 square root of 14dy - 10ysquare root of 14d
e A LaTex expression showing 5{d} to the power of 4 {y} to the power of 2 square root of 14y - 10dysquare root of 14d
8
Multiply the radical expressions and simplify the answer
A LaTex expression showing (3zdsquare root of 3d - {d} to the power of 2 square root of 13) times 4square root of 11zd
a A LaTex expression showing 12z{d} to the power of 2 square root of 33z - 4square root of 143zd
b A LaTex expression showing 12z{d} to the power of 2 square root of 33z - 4dsquare root of 143zd
c A LaTex expression showing 12z{d} to the power of 2 square root of 33z - 4{d} to the power of 2 square root of 143zd
d A LaTex expression showing 12z{d} to the power of 2 square root of 33z - 4{d} to the power of 3 square root of 143zd
e A LaTex expression showing 12{z} to the power of -1 {d} to the power of 2 square root of 33z - 4{d} to the power of 2 square root of 143zd