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Radicals - Multiplying Binomials (Values and Variables) (Level 2)

This math topic focuses on practicing the multiplication of binomial expressions that contain radicals, involving variables and constants. It covers expanding and simplifying the products of binomial expressions which comprise square roots and variable terms at a more advanced level, possibly including the distribution of squared and cubed terms. Each problem sets up expressions in a format inviting the student to carry out the multiplication and then choose the correctly simplified form from multiple choices, ensuring a comprehensive understanding and application of radical manipulation rules in algebra.

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

(n7+2)⋅(3−5)(n\sqrt{7} + \sqrt{2}) \cdot (\sqrt{3} - \sqrt{5})

Radicals - Multiplying Binomials (Values and Variables) Worksheet

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Math worksheet on 'Radicals - Multiplying Binomials (Values and Variables) (Level 2)'. 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 (csquare root of 3 + {c} to the power of 2 square root of 5) times (csquare root of 7 + csquare root of 3c)
a A LaTex expression showing {c} to the power of 2 square root of 21 + 3{c} to the power of 2 square root of c + {c} to the power of 3 square root of 35 + {c} to the power of 3 square root of 15c
b A LaTex expression showing {c} to the power of 2 square root of 21 + 3{c} to the power of 3 + {c} to the power of 3 square root of 35 - {c} to the power of 3 square root of 15c
c A LaTex expression showing {c} to the power of 2 square root of 21 - 3{c} to the power of 2 square root of c + 3{c} to the power of 3 square root of 35 + {c} to the power of 3 square root of 15c
d A LaTex expression showing csquare root of 21 + {c} to the power of 2 square root of c + {c} to the power of 3 square root of 35 + {c} to the power of 3 square root of 15c
e A LaTex expression showing {c} to the power of 2 square root of 21 + 3{c} to the power of 2 square root of {c to the power of -1 } - {c} to the power of 3 + {c} to the power of 3 square root of 15c
f A LaTex expression showing 4{c} to the power of 2 square root of 21 + 3{c} to the power of 2 square root of c + {c} to the power of 5 square root of 35 + {c} to the power of 3 square root of 15c
2
Multiply the radical expressions and simplify the answer
A LaTex expression showing (nsquare root of 7 + square root of 2) times (square root of 3 - square root of 5)
a A LaTex expression showing nsquare root of 21 - {n} to the power of 2 square root of 35 + square root of 6 - square root of 10
b A LaTex expression showing nsquare root of 21 - nsquare root of 35 + square root of 6 - square root of 10
c A LaTex expression showing nsquare root of 21 + nsquare root of 35 + 1
d A LaTex expression showing square root of 6 + square root of 10
e A LaTex expression showing {n} to the power of -1 square root of 21 - nsquare root of 35 + square root of 2 + square root of 10
f A LaTex expression showing {n} to the power of -1 square root of 21 - nsquare root of 35 + square root of 6 + 5square root of 10
3
A LaTex expression showing (msquare root of 5m + msquare root of 3) times (square root of 13 - msquare root of 2m)
Multiply the radical expressions and simplify the answer
a A LaTex expression showing msquare root of 65 - {m} to the power of 3 square root of 10 + m - {m} to the power of 2 square root of 6m
b A LaTex expression showing msquare root of 65m + {m} to the power of 3 square root of 10 + m - {m} to the power of 2 square root of m
c A LaTex expression showing msquare root of 65{m to the power of -1 } - {m} to the power of 3 square root of 10 + msquare root of 39 - {m} to the power of 2 square root of 6
d A LaTex expression showing msquare root of 65m + {m} to the power of 3 square root of 10 + msquare root of 39 - {m} to the power of 2 square root of 6m
e A LaTex expression showing msquare root of 65m - {m} to the power of 3 square root of 10 + msquare root of 39 - {m} to the power of 3 square root of 6
f A LaTex expression showing msquare root of 65m - {m} to the power of 3 square root of 10 + msquare root of 39 - {m} to the power of 2 square root of 6m
4
Multiply the radical expressions and simplify the answer
A LaTex expression showing (rsquare root of 3 - rsquare root of 13) times ({r} to the power of 2 square root of 7 - square root of 3r)
a A LaTex expression showing {r} to the power of 4 square root of 21 - 3{r} to the power of 2 square root of r - {r} to the power of 3 square root of 91 - rsquare root of 39r
b A LaTex expression showing {r} to the power of 3 square root of 21 - 3rsquare root of r - {r} to the power of 3 square root of 91 + rsquare root of 39r
c A LaTex expression showing {r} to the power of 3 square root of 21 - 3{r} to the power of 2 square root of r - {r} to the power of 3 square root of 91 + rsquare root of 39r
d A LaTex expression showing {r} to the power of 3 square root of 21 - 3rsquare root of r - rsquare root of 91 + rsquare root of 39r
e A LaTex expression showing {r} to the power of 4 square root of 21 - 3rsquare root of {r to the power of -1 } + {r} to the power of 3 square root of 91 + rsquare root of 39r
f A LaTex expression showing {r} to the power of 3 square root of 21 - 9rsquare root of r - {r} to the power of 3 square root of 91 + {r} to the power of -1 square root of 39r
5
Multiply the radical expressions and simplify the answer
A LaTex expression showing (square root of 5c - csquare root of 13c) times (csquare root of 2 + csquare root of 13)
a A LaTex expression showing csquare root of 10 + csquare root of 65 + {c} to the power of 2 square root of 26c - 13{c} to the power of 2 square root of c
b A LaTex expression showing csquare root of 10c + square root of 65c - {c} to the power of 2 square root of 26{c to the power of -1 } - 13{c} to the power of 2 square root of c
c A LaTex expression showing csquare root of 10c + csquare root of 65{c to the power of -1 } - {c} to the power of 2 square root of 26c - 13{c} to the power of 2 square root of c
d A LaTex expression showing csquare root of 10c + csquare root of 65c + 12{c} to the power of 2 square root of c
e A LaTex expression showing csquare root of 10c + csquare root of 65c - {c} to the power of 2 square root of 26c - 13{c} to the power of 2 square root of c
f A LaTex expression showing csquare root of 10c + csquare root of 65{c to the power of -3 } - {c} to the power of 2 square root of 26c - 13{c} to the power of 2 square root of c
6
A LaTex expression showing (msquare root of 2m + msquare root of 3m) times (square root of 5 + msquare root of 3m)
Multiply the radical expressions and simplify the answer
a A LaTex expression showing msquare root of 10m - {m} to the power of 4 square root of 6 + msquare root of 3m + 3{m} to the power of 3
b A LaTex expression showing msquare root of 10m + {m} to the power of 3 square root of 6 + msquare root of 15m + 3{m} to the power of 3
c A LaTex expression showing msquare root of 10m + {m} to the power of 4 square root of 6 + {m} to the power of 2 square root of 15 + 3{m} to the power of 3
d A LaTex expression showing msquare root of 10m + {m} to the power of 5 square root of 6 + {m} to the power of 2 square root of 15 + 3{m} to the power of 3
e A LaTex expression showing msquare root of 10m + {m} to the power of 3 square root of 6 + 3msquare root of 15 + 3{m} to the power of 3
f A LaTex expression showing {m} to the power of 2 square root of 10m + {m} to the power of 3 square root of 6m + msquare root of 15m - 3{m} to the power of 3
7
A LaTex expression showing (nsquare root of 13 + nsquare root of 2n) times (square root of 13 - square root of 5n)
Multiply the radical expressions and simplify the answer
a A LaTex expression showing 13n + nsquare root of 26n - nsquare root of 65n + {n} to the power of 2 square root of 10
b A LaTex expression showing 13n + nsquare root of 26n + {n} to the power of -1 square root of 65{n to the power of -1 } - {n} to the power of 2 square root of 10
c A LaTex expression showing 13n - nsquare root of 26n - nsquare root of 65 - {n} to the power of 2 square root of 10
d A LaTex expression showing 1 + nsquare root of 26n - nsquare root of 65n - {n} to the power of 2 square root of 10
e A LaTex expression showing 13n + square root of 26n - nsquare root of n - {n} to the power of 2 square root of 10
f A LaTex expression showing 13n + nsquare root of 26n - nsquare root of 65n - {n} to the power of 2 square root of 10