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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

(13−37)⋅(11+213)(\sqrt{13} - 3\sqrt{7}) \cdot (\sqrt{11} + 2\sqrt{13})

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 (4square root of 2 + square root of 11) times (square root of 2 + 3square root of 7)
a A LaTex expression showing 4square root of 3 + square root of 22 + 12square root of 14 - 2square root of 77
b A LaTex expression showing 9 + 12square root of 14 + 3
c A LaTex expression showing 5 + square root of 22 - 12square root of 14
d A LaTex expression showing 8 + square root of 22 + 12square root of 14 + 3square root of 77
e A LaTex expression showing 14 - square root of 22 + 3square root of 77
f A LaTex expression showing square root of 2 + square root of 22 + 12square root of 14 - 3square root of 77
2
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 square root of 14 - 3square root of 91 + 4 - square root of 39
b A LaTex expression showing 8square root of 2 - 3square root of 91 - square root of 39
c A LaTex expression showing 12square root of 14 - 3square root of 91 + square root of 6 - 3square root of 39
d A LaTex expression showing 12square root of 14 - 3square root of 91 + 4square root of 6 - square root of 39
e A LaTex expression showing 12square root of 14 - 3 + 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
3
Multiply the radical expressions and simplify the answer
A LaTex expression showing (2square root of 7 + square root of 3) times (square root of 11 - 5square root of 2)
a A LaTex expression showing 2square root of 77 + 4square root of 14 + square root of 33 - 5
b A LaTex expression showing 2 - 10square root of 14 + square root of 33 - 5square root of 6
c A LaTex expression showing 2square root of 77 - 10square root of 14 + square root of 33 - 5square root of 6
d A LaTex expression showing 2square root of 77 - 3square root of 14 - square root of 33 - 5square root of 3
e A LaTex expression showing 2square root of 77 - square root of 14 + square root of 33 - square root of 6
f A LaTex expression showing 5square root of 77 - 10 + square root of 33 - 5square root of 6
4
Multiply the radical expressions and simplify the answer
A LaTex expression showing (square root of 7 - 5square root of 5) times (square root of 11 + 2square root of 7)
a A LaTex expression showing square root of 77 + 2 - 10square root of 35
b A LaTex expression showing 3 + 5square root of 55 - 10square root of 35
c A LaTex expression showing square root of 77 + 14 - 5square root of 55 - 10square root of 35
d A LaTex expression showing square root of 77 + 9 - 2square root of 35
e A LaTex expression showing 15 + 2square root of 55 - 10square root of 35
f A LaTex expression showing square root of 77 + 14 - square root of 55 - square root of 35
5
Multiply the radical expressions and simplify the answer
A LaTex expression showing (3square root of 3 + square root of 3) times (square root of 7 + 2square root of 7)
a A LaTex expression showing 3 + 2square root of 21 + 2square root of 21
b A LaTex expression showing 7square root of 21 + 2square root of 21
c A LaTex expression showing 9square root of 21 + 1 + 2square root of 21
d A LaTex expression showing 6square root of 21 + 6 + 2square root of 21
e A LaTex expression showing 9square root of 21 + 3square root of 21
f A LaTex expression showing 9square root of 21 + 3
6
Multiply the radical expressions and simplify the answer
A LaTex expression showing (3square root of 11 + square root of 5) times (square root of 2 - 2square root of 7)
a A LaTex expression showing 3square root of 22 + square root of 10 - square root of 77 - 2square root of 2
b A LaTex expression showing 3square root of 22 - square root of 10 - 6square root of 77 + square root of 35
c A LaTex expression showing 3square root of 22 + square root of 10 - 4square root of 77 - 2square root of 35
d A LaTex expression showing 3square root of 22 + square root of 10 + 6square root of 77 - square root of 35
e A LaTex expression showing 3square root of 22 + square root of 10 - 6square root of 77 - 2square root of 35
f A LaTex expression showing 3square root of 22 + square root of 10 - 3square root of 77 - 2square root of 35
7
Multiply the radical expressions and simplify the answer
A LaTex expression showing (3square root of 5 + square root of 2) times (square root of 5 - 3square root of 11)
a A LaTex expression showing 20 + square root of 55 + square root of 10 - 3square root of 22
b A LaTex expression showing 14 + square root of 10 - 3square root of 22
c A LaTex expression showing 25 - 9square root of 55 + square root of 10 - 3square root of 22
d A LaTex expression showing 15 - 9square root of 55 - square root of 10 + square root of 22
e A LaTex expression showing 15 - 9square root of 55 + square root of 10 - 3square root of 22
f A LaTex expression showing 16 - 9square root of 55 + square root of 22