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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

(4c+7c)â‹…(5c+13)(4\sqrt{c} + \sqrt{7c}) \cdot (5\sqrt{c} + \sqrt{13})

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 (2 - bsquare root of 13) times (4bsquare root of b - square root of 11b)
a A LaTex expression showing 8bsquare root of b - 4{b} to the power of 2 square root of 13b - 2square root of 11b + bsquare root of 143b
b A LaTex expression showing 8bsquare root of b + {b} to the power of 2 square root of 13b - 2bsquare root of 11 + bsquare root of 143b
c A LaTex expression showing 8bsquare root of b - 4{b} to the power of 2 square root of b + 2square root of 11b + {b} to the power of 2 square root of 143b
d A LaTex expression showing 8bsquare root of {b to the power of -1 } - 4{b} to the power of 4 square root of 13b - 2square root of 11b + bsquare root of 143b
e A LaTex expression showing 8{b} to the power of 3 square root of b - 4{b} to the power of 2 square root of 13b - 2square root of 11b + {b} to the power of 2 square root of 143
f A LaTex expression showing 8{b} to the power of 3 square root of b - {b} to the power of 2 square root of 13b - 2square root of 11b + bsquare root of 143b
2
Multiply the radical expressions and simplify the answer
A LaTex expression showing (3 - {p} to the power of 2 square root of 5) times (square root of 11 - 3p)
a A LaTex expression showing 3square root of 11 - 9p - {p} to the power of 2 square root of 55 + 3{p} to the power of 3 square root of 5
b A LaTex expression showing 3square root of 11 - 9p - {p} to the power of 4 square root of 55 + 3{p} to the power of 3 square root of 5
c A LaTex expression showing 3square root of 11 - 9p + {p} to the power of 2 square root of 55 - {p} to the power of 3 square root of 5
d A LaTex expression showing 4square root of 11 + 9p - {p} to the power of 2 square root of 55 + 3{p} to the power of 3 square root of 5
e A LaTex expression showing square root of 11 + 9p - {p} to the power of 2 square root of 55 + 3{p} to the power of 3
f A LaTex expression showing 3 - 9p - {p} to the power of 2 square root of 55 + 3psquare root of 5
3
A LaTex expression showing ({x} to the power of 2 square root of 11 + 3square root of x) times (square root of 3 - 5xsquare root of x)
Multiply the radical expressions and simplify the answer
a A LaTex expression showing -14{x} to the power of 2 - 5{x} to the power of 3 square root of 11x + square root of 3x
b A LaTex expression showing {x} to the power of 2 square root of 33 + 5{x} to the power of 3 square root of 11x + square root of 3{x to the power of -1 } - 15{x} to the power of 2
c A LaTex expression showing {x} to the power of 2 square root of 33 - 5{x} to the power of 3 square root of 11x + 3square root of 3x - 15{x} to the power of 2
d A LaTex expression showing {x} to the power of 2 square root of 33 + 5{x} to the power of 3 square root of 11x + 3square root of 3x - 15{x} to the power of 2
e A LaTex expression showing {x} to the power of 2 square root of 33 - 5{x} to the power of 3 square root of 11x + 5square root of x - 15{x} to the power of 2
f A LaTex expression showing {x} to the power of 2 square root of 33 - {x} to the power of 3 square root of 11x + 3square root of x - 15{x} to the power of 2
4
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 2 - 5square root of 13 + 25{r} to the power of 2
c 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
d 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
e 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
f A LaTex expression showing 3square root of 39 + 30{r} to the power of 2 + 5square root of 13
5
Multiply the radical expressions and simplify the answer
A LaTex expression showing (2 + msquare root of 7) times (2 - {m} to the power of 2 square root of 13)
a A LaTex expression showing 4 - 2msquare root of 7 - 2{m} to the power of 2 square root of 3 + {m} to the power of 3
b A LaTex expression showing 4 + 2msquare root of 7 - 2{m} to the power of 2 square root of 13 - {m} to the power of 3 square root of 91
c A LaTex expression showing 4 + 2m - 2{m} to the power of 2 square root of 13 - {m} to the power of 2 square root of 91
d A LaTex expression showing 4 + 2msquare root of 7 + 2{m} to the power of 2 square root of 13 - {m} to the power of 5 square root of 91
e A LaTex expression showing 4 + msquare root of 7 - 2{m} to the power of 2 - {m} to the power of 3 square root of 91
f A LaTex expression showing 4 + 2square root of 7 - 2{m} to the power of 2 square root of 13 - {m} to the power of 3 square root of 91
6
Multiply the radical expressions and simplify the answer
A LaTex expression showing (5square root of p + square root of 11) times (3psquare root of p - square root of 7)
a A LaTex expression showing 15{p} to the power of 2 + 3psquare root of 11 - square root of 7p - square root of 77
b A LaTex expression showing 15{p} to the power of 2 + 3psquare root of 11p - 5square root of 7 - 1
c A LaTex expression showing 15{p} to the power of 4 - 3psquare root of 11p - 3square root of 7p + square root of 77
d A LaTex expression showing 15{p} to the power of 2 + 3psquare root of 11p - 5square root of 7p - square root of 77
e A LaTex expression showing 15{p} to the power of 2 + 3psquare root of 11p - square root of 7p + square root of 77
f A LaTex expression showing 15{p} to the power of 2 square root of p + 3psquare root of 11p - 5square root of 7 - square root of 77
7
Multiply the radical expressions and simplify the answer
A LaTex expression showing ({z} to the power of 2 square root of 5 - 3{z} to the power of 2 ) times (zsquare root of 7z - 2)
a A LaTex expression showing {z} to the power of 3 square root of 35z - 2{z} to the power of 2 square root of 5 - 3{z} to the power of 4 square root of 7 + 6
b A LaTex expression showing {z} to the power of 5 square root of 35z - 2{z} to the power of 4 square root of 5 - 3{z} to the power of 3 square root of 7z + 6{z} to the power of 2
c A LaTex expression showing {z} to the power of 3 square root of 35z - 2{z} to the power of 2 square root of 5 - 3{z} to the power of 3 square root of 7z + 6{z} to the power of 2
d A LaTex expression showing {z} to the power of 3 square root of 35z - 2{z} to the power of 4 square root of 5 + 3{z} to the power of 3 square root of 7z + 6{z} to the power of 2
e A LaTex expression showing {z} to the power of 3 square root of 35z + 2{z} to the power of 3 - 3{z} to the power of 3 square root of 7z + 6{z} to the power of 2
f A LaTex expression showing {z} to the power of 3 square root of 35z + 4{z} to the power of 2 - 3{z} to the power of 4 square root of 7