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Radicals - Multiplying Binomials (Values and Variables) (Level 1)

This math topic focuses on practicing the multiplication of radical expressions involving binomials that include both numerical and variable components. The skills developed entail expanding and simplifying algebraic expressions that feature radicals and a variety of operations such as addition, subtraction, and multiplication. Each problem is presented with multiple-choice answers for students to select the correctly simplified version of the radical product. The main theme of these problems is not only to perform the multiplication accurately but also to apply the rules for simplifying square roots and combining like terms.

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

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Multiplying 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

(r13r+5r)⋅(r3r−2r)(r\sqrt{13r} + 5\sqrt{r}) \cdot (r\sqrt{3r} - 2r)

Radicals - Multiplying Binomials (Values and Variables) Worksheet

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Math worksheet on 'Radicals - Multiplying Binomials (Values and Variables) (Level 1)'. 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 (3csquare root of c + csquare root of 2c) times (square root of 5 + 4csquare root of c)
a A LaTex expression showing 3{c} to the power of -1 square root of 5c + 12{c} to the power of 3 + csquare root of 10c + 4csquare root of 2
b A LaTex expression showing 3csquare root of 5c + 12{c} to the power of 3 + csquare root of 10c - 5csquare root of 2
c A LaTex expression showing 3csquare root of 5c + 12{c} to the power of 3 + csquare root of 10c + 4{c} to the power of 3 square root of 2
d A LaTex expression showing 3csquare root of 5c - 12{c} to the power of 2 + {c} to the power of 2 square root of 10c + 4{c} to the power of 3 square root of 2
e A LaTex expression showing csquare root of 5c - 12{c} to the power of 2 + csquare root of 10c + 4{c} to the power of 3 square root of 2
f A LaTex expression showing 3csquare root of 5c + 12{c} to the power of 3 + csquare root of 10c - 4csquare root of 2
2
Multiply the radical expressions and simplify the answer
A LaTex expression showing (2 - square root of 11) times (3n + square root of 5)
a A LaTex expression showing n - 3nsquare root of 11 + 2square root of 5 + 1
b A LaTex expression showing 6{n} to the power of 2 + 5nsquare root of 11 + 2square root of 5 - square root of 55
c A LaTex expression showing 6n - 3nsquare root of 11 - 2square root of 5 + square root of 55
d A LaTex expression showing 6n - 3nsquare root of 11 + 2square root of 5 - 1
e A LaTex expression showing 6n - 3nsquare root of 11 + 2square root of 5 - square root of 55
f A LaTex expression showing 6n + 3nsquare root of 11 + 4square root of 5 - square root of 55
3
A LaTex expression showing (square root of 5 - 5nsquare root of n) times ({n} to the power of 2 square root of 13 - 4nsquare root of n)
Multiply the radical expressions and simplify the answer
a A LaTex expression showing {n} to the power of 2 square root of 65 - 4nsquare root of 5n - 5{n} to the power of 5 square root of 13n + 20{n} to the power of 3
b A LaTex expression showing {n} to the power of 2 square root of 65 + 4nsquare root of 5 - 5{n} to the power of 3 square root of 13 + 20{n} to the power of 3
c A LaTex expression showing {n} to the power of 2 square root of 65 - 4nsquare root of 5n + 5{n} to the power of 3 square root of {n to the power of -1 } + 20{n} to the power of 3
d A LaTex expression showing {n} to the power of 2 square root of 65 - 4nsquare root of 5n + 5{n} to the power of 3 square root of 13n + 20{n} to the power of 3
e A LaTex expression showing {n} to the power of 2 square root of 65 - 4nsquare root of 5n - 5{n} to the power of 3 square root of 13n + 20{n} to the power of 3
f A LaTex expression showing {n} to the power of 2 square root of 65 + {n} to the power of 2 square root of 5 - 5{n} to the power of 3 square root of 13n - 20{n} to the power of 3
4
Multiply the radical expressions and simplify the answer
A LaTex expression showing (4x - square root of 2x) times (square root of 7x + 5{x} to the power of 2 )
a A LaTex expression showing 4xsquare root of 7x + xsquare root of 14 + 20x - 5{x} to the power of 2 square root of 2x
b A LaTex expression showing 4xsquare root of 7x - xsquare root of 14 + 20x + 5xsquare root of 2x
c A LaTex expression showing 4xsquare root of 7 - xsquare root of 14 + 20{x} to the power of 3 - 5{x} to the power of 3 square root of 2
d A LaTex expression showing 4xsquare root of 7x - x - 20{x} to the power of 3 - 5{x} to the power of 2 square root of 2x
e A LaTex expression showing 4xsquare root of 7x - xsquare root of 14 - 20{x} to the power of 5 - 5{x} to the power of 3 square root of 2x
f A LaTex expression showing 4xsquare root of 7x - xsquare root of 14 + 20{x} to the power of 3 - 5{x} to the power of 2 square root of 2x
5
Multiply the radical expressions and simplify the answer
A LaTex expression showing (4 + square root of 3) times (4 - square root of 5)
a A LaTex expression showing 16 + square root of 3 + 4square root of 5 - square root of 15
b A LaTex expression showing 16 + 4square root of 3 - square root of 5 - square root of 15
c A LaTex expression showing 17 + 4square root of 3 - 4square root of 5
d A LaTex expression showing 16 + 4square root of 3 - 4square root of 5 - square root of 15
e A LaTex expression showing 16 - 4square root of 3 + 4square root of 5 - square root of 15
f A LaTex expression showing 1 - square root of 3 - 4square root of 5 + square root of 15
6
Multiply the radical expressions and simplify the answer
A LaTex expression showing (square root of 3 + 5) times (square root of 13 + 5{r} to the power of 2 )
a A LaTex expression showing square root of 39 + 2{r} to the power of 3 square root of 3 - 5square root of 13 + 25{r} to the power of 2
b A LaTex expression showing 1 + 5{r} to the power of 2 square root of 3 - 5square root of 13 + 25{r} to the power of 2
c A LaTex expression showing 3square root of 39 + 30{r} to the power of 2 + 5square root of 13
d A LaTex expression showing square root of 39 + 2{r} to the power of 2 square root of 3 + square root of 13 - 25{r} to the power of 2
e A LaTex expression showing 1 + 5{r} to the power of 2 square root of 2 - 5square root of 13 + 25{r} to the power of 2
f A LaTex expression showing square root of 39 + 5{r} to the power of 2 square root of 3 + 5square root of 13 + 25{r} to the power of 2
7
Multiply the radical expressions and simplify the answer
A LaTex expression showing (4zsquare root of z + zsquare root of 5) times (square root of 3z - 5z)
a A LaTex expression showing 4zsquare root of 3 - 20{z} to the power of 2 square root of z + zsquare root of 15z - 5{z} to the power of 2 square root of 5
b A LaTex expression showing 4{z} to the power of 2 square root of 3 - {z} to the power of 3 + zsquare root of 15z - 5{z} to the power of 2 square root of 5
c A LaTex expression showing 4zsquare root of 3 + 20zsquare root of z - zsquare root of 15z - 5{z} to the power of 2 square root of 5
d A LaTex expression showing {z} to the power of 2 square root of 3 - 40{z} to the power of 2 square root of z - zsquare root of 15z + 5{z} to the power of 2 square root of 5
e A LaTex expression showing 4{z} to the power of 2 square root of 3 - {z} to the power of 2 + zsquare root of 15z - 5{z} to the power of 2 square root of 5
f A LaTex expression showing 4{z} to the power of 2 square root of 3 - 20{z} to the power of 2 square root of z + zsquare root of 15z - 5{z} to the power of 2 square root of 5