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Radicals - Multiplying Binomials (Values Only) (Level 3)

This math topic focuses on multiplying binomials involving radical expressions and simplifying the results. It falls under a broader introduction to radical multiplication, enhancing skills in handling square roots combined with integer and other square root terms. The problems require multiplying binomials, each containing radicals, and simplifying them to the simplest possible form with provided multiple-choice answers. Each question includes different binomial expressions featuring square roots combined with various constants, demonstrating the application of the distributive property (FOIL method) in radical equations.

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

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Multiplying Binomials (Values Only)

Complete these online problems with 80% or 4 correct answers in a row. Results are immediate.

Multiply the radical expressions and simplify the answer

(42+11)⋅(11−53)(4\sqrt{2} + \sqrt{11}) \cdot (\sqrt{11} - 5\sqrt{3})

Radicals - Multiplying Binomials (Values Only) Worksheet

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Math worksheet on 'Radicals - Multiplying Binomials (Values Only) (Level 3)'. 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 (3square root of 2 - square root of 11) times (square root of 2 + 4square root of 7)
a A LaTex expression showing 2 + 12square root of 14 - 4square root of 77
b A LaTex expression showing 2 + 12square root of 14 - square root of 22 - 4square root of 77
c A LaTex expression showing 2 + 12square root of 14 - 4square root of 22
d A LaTex expression showing 6 - 12square root of 14 - square root of 22 - square root of 77
e A LaTex expression showing 14 + square root of 22 + 4square root of 77
f A LaTex expression showing 6 + 12square root of 14 - square root of 22 - 4square root of 77
2
Multiply the radical expressions and simplify the answer
A LaTex expression showing (2square root of 5 + square root of 5) times (square root of 2 + 4square root of 11)
a A LaTex expression showing 3square root of 10 + 5square root of 55
b A LaTex expression showing 2 - square root of 10 + 12square root of 55
c A LaTex expression showing 3square root of 10 + 8 + 4square root of 55
d A LaTex expression showing 3square root of 10 + 12square root of 55
e A LaTex expression showing 2square root of 10 + 6square root of 55
f A LaTex expression showing 3square root of 10 + 1 + 4square root of 55
3
Multiply the radical expressions and simplify the answer
A LaTex expression showing (square root of 3 + 3square root of 7) times (square root of 3 - 5square root of 2)
a A LaTex expression showing -12 - 5square root of 6 + 3square root of 21
b A LaTex expression showing 3 - 5square root of 6 + 3square root of 21 - square root of 14
c A LaTex expression showing 3 - 5square root of 6 + 3square root of 21 - 15square root of 14
d A LaTex expression showing 3 - square root of 6 - 3square root of 21 + 15square root of 14
e A LaTex expression showing 3 - 5square root of 6 - 3square root of 21 - 15square root of 14
f A LaTex expression showing 3 - 4square root of 6 + 4square root of 21 - 15square root of 14
4
Multiply the radical expressions and simplify the answer
A LaTex expression showing (4square root of 2 - square root of 13) times (3square root of 7 + square root of 3)
a A LaTex expression showing 8square root of 2 - 3square root of 91 - square root of 39
b A LaTex expression showing 12square root of 14 - 3 + 4square root of 6 - square root of 39
c A LaTex expression showing square root of 14 - 3square root of 91 + 4 - square root of 39
d A LaTex expression showing 12square root of 14 - 3square root of 91 + square root of 6 - 3square root of 39
e A LaTex expression showing 12square root of 14 - 3square root of 91 + 4square root of 6 - square root of 39
f A LaTex expression showing square root of 14 - square root of 91 + 4square root of 6 - square root of 39
5
Multiply the radical expressions and simplify the answer
A LaTex expression showing (4square root of 3 - square root of 13) times (4square root of 3 + square root of 5)
a A LaTex expression showing 48 - square root of 39 - 4square root of 15 - square root of 65
b A LaTex expression showing 19 - 4square root of 39 + square root of 65
c A LaTex expression showing 44 - 2square root of 15 - square root of 65
d A LaTex expression showing 10 - 4square root of 39 + square root of 65
e A LaTex expression showing 48 - 4square root of 39 + 4square root of 15 - square root of 65
f A LaTex expression showing 48 - square root of 39 - 4square root of 15 + square root of 65
6
Multiply the radical expressions and simplify the answer
A LaTex expression showing (square root of 13 - 3square root of 7) times (square root of 11 + 2square root of 13)
a A LaTex expression showing square root of 143 + 26 - 3square root of 77 - 6square root of 91
b A LaTex expression showing square root of 143 + 13 - square root of 77 - 6square root of 91
c A LaTex expression showing square root of 143 - 25 - 3square root of 77
d A LaTex expression showing square root of 143 + 21 - 6square root of 91
e A LaTex expression showing square root of 143 - 29 - 6square root of 91
f A LaTex expression showing 27 + square root of 77 - 6square root of 91
7
Multiply the radical expressions and simplify the answer
A LaTex expression showing (3square root of 5 - square root of 11) times (square root of 11 + 2square root of 13)
a A LaTex expression showing 3square root of 55 - 6square root of 65 - 1 - 2square root of 143
b A LaTex expression showing square root of 55 + 2square root of 65 - 11 - 2square root of 143
c A LaTex expression showing 3square root of 55 + 6square root of 65 - 1 - 5square root of 143
d A LaTex expression showing 3square root of 55 + 6square root of 65 - 11 + square root of 143
e A LaTex expression showing 3square root of 55 + 6square root of 65 - 11 - 2square root of 143
f A LaTex expression showing 3square root of 55 + 2square root of 65 - 1 - 2square root of 143