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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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 (square root of 5 - 3) times (square root of 2p + 2square root of p)
a A LaTex expression showing square root of 10p + 2square root of 5p - 3square root of 2{p to the power of -2 } - 6square root of p
b A LaTex expression showing square root of 10{p to the power of -3 } + 2square root of 5p - 3square root of 2p - 6square root of p
c A LaTex expression showing square root of 10p + 2square root of 5p - 3psquare root of 2 - 6square root of p
d A LaTex expression showing square root of 10p + 2square root of 5p - 3square root of 2p - 6square root of p
e A LaTex expression showing psquare root of 10 + 2square root of 5p - 3square root of 2 + 6square root of p
2
Multiply the radical expressions and simplify the answer
A LaTex expression showing (5square root of z - square root of 11z) times (3square root of z + {z} to the power of 2 square root of 5)
a A LaTex expression showing 15square root of z - zsquare root of 11 + 5{z} to the power of 2 square root of 5z + {z} to the power of 2 square root of 55z
b A LaTex expression showing 15z - 3zsquare root of 11 + {z} to the power of 2 square root of 5z - {z} to the power of 3 square root of 55
c A LaTex expression showing 15z - 3zsquare root of 11z - {z} to the power of 2 square root of 5z - {z} to the power of 2 square root of 55z
d A LaTex expression showing 15z - 3zsquare root of 11 + 5{z} to the power of 2 square root of 5z - {z} to the power of 2 square root of 55z
e A LaTex expression showing 13z - 5{z} to the power of 2 square root of 5z + {z} to the power of 2 square root of 55z
3
A LaTex expression showing (5xsquare root of x + {x} to the power of 2 square root of 13) times (square root of 7x - 3xsquare root of x)
Multiply the radical expressions and simplify the answer
a A LaTex expression showing 5xsquare root of 7x + {x} to the power of 2 square root of 91x - 15{x} to the power of 2 + 3{x} to the power of 3 square root of 13x
b A LaTex expression showing 5{x} to the power of 2 square root of 7 + {x} to the power of 2 square root of 91x - 15{x} to the power of 3 - 3{x} to the power of 3 square root of 13
c A LaTex expression showing 5{x} to the power of 2 square root of 7 + {x} to the power of 2 square root of 91x + 15{x} to the power of 2 square root of x - 3{x} to the power of 4 square root of 13x
d A LaTex expression showing 5{x} to the power of 2 square root of 7 + {x} to the power of 2 square root of 91x - 15{x} to the power of 3 - 3{x} to the power of 3 square root of 13x
e A LaTex expression showing 5{x} to the power of 2 square root of 7 + {x} to the power of 2 square root of 91x - 15{x} to the power of 3 + 3{x} to the power of 3 square root of 13
4
Multiply the radical expressions and simplify the answer
A LaTex expression showing (square root of 7r + 4r) times ({r} to the power of 2 square root of 5 - 4r)
a A LaTex expression showing {r} to the power of 2 square root of 35r - 4rsquare root of 7r + 4{r} to the power of 3 square root of 5 - 16{r} to the power of 2
b A LaTex expression showing {r} to the power of 4 square root of 35r + 4rsquare root of 7 + 4{r} to the power of 3 square root of 5 - 16{r} to the power of 2
c A LaTex expression showing rsquare root of 35r - 4{r} to the power of 2 square root of 7r + 4{r} to the power of 3 square root of 5 - 16{r} to the power of 2
d A LaTex expression showing {r} to the power of 2 square root of r + 4rsquare root of 7r - {r} to the power of 3 square root of 5 - 16{r} to the power of 2
e A LaTex expression showing {r} to the power of 2 square root of 35{r to the power of -1 } - 4{r} to the power of 2 square root of 7 + 4{r} to the power of 3 square root of 5 - 16{r} to the power of 2
5
Multiply the radical expressions and simplify the answer
A LaTex expression showing (4square root of p + {p} to the power of 2 square root of 2) times (square root of 7p - 2psquare root of p)
a A LaTex expression showing psquare root of 7 + 8{p} to the power of 2 + {p} to the power of 4 square root of 14p - 2{p} to the power of 3 square root of 2p
b A LaTex expression showing psquare root of 7 - 8{p} to the power of 2 + {p} to the power of 3 square root of 14 - 2{p} to the power of 3 square root of 2p
c A LaTex expression showing 4p - 8{p} to the power of 2 + {p} to the power of 2 square root of 14p + 2{p} to the power of 3 square root of p
d A LaTex expression showing 4psquare root of 7 - 8{p} to the power of 3 - {p} to the power of 3 square root of 14p - 2{p} to the power of 3 square root of 2p
e A LaTex expression showing 4psquare root of 7 - 8{p} to the power of 2 + {p} to the power of 2 square root of 14p - 2{p} to the power of 3 square root of 2p
6
Multiply the radical expressions and simplify the answer
A LaTex expression showing (4c + square root of 13c) times (square root of 7c + 3csquare root of c)
a A LaTex expression showing 4csquare root of 7c + 12{c} to the power of 2 square root of c + csquare root of 91 + 4{c} to the power of 4 square root of 13
b A LaTex expression showing 4csquare root of 7c + 12{c} to the power of 2 square root of c + square root of 91 + 3csquare root of 13
c A LaTex expression showing 4csquare root of 7c + 12{c} to the power of 2 square root of c + csquare root of 91 + 3{c} to the power of 2 square root of 13
d A LaTex expression showing 4csquare root of 7c + 12{c} to the power of 2 square root of c + square root of 91c - 3{c} to the power of 3 square root of 13
e A LaTex expression showing 4csquare root of 7c + 12{c} to the power of 3 square root of c + csquare root of 91 + 3csquare root of 13
7
Multiply the radical expressions and simplify the answer
A LaTex expression showing (3{b} to the power of 2 - {b} to the power of 2 square root of 7) times (bsquare root of 2b - 4{b} to the power of 2 )
a A LaTex expression showing 3{b} to the power of 3 square root of 2 - {b} to the power of 3 square root of 14b - 12{b} to the power of 4 + 4{b} to the power of 2 square root of 7
b A LaTex expression showing 3{b} to the power of 3 square root of 2b - {b} to the power of 3 square root of b - 12{b} to the power of 4 + 4{b} to the power of 5 square root of 7
c A LaTex expression showing 3{b} to the power of 3 square root of 2b - bsquare root of 14b + 12{b} to the power of 4 + 4{b} to the power of 5 square root of 7
d A LaTex expression showing 3{b} to the power of 3 square root of 2b - {b} to the power of 3 square root of 14b - 12{b} to the power of 4 + 4{b} to the power of 4 square root of 7
e A LaTex expression showing 3{b} to the power of 3 square root of 2b - {b} to the power of 3 square root of 14b - 12b + 4{b} to the power of 4 square root of 7