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Radical

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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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 (rsquare root of 3 + square root of 3r) times (rsquare root of 13 - square root of 13)
a A LaTex expression showing {r} to the power of 3 square root of 39 - rsquare root of 39
b A LaTex expression showing 2{r} to the power of 2 - 2rsquare root of 39 + rsquare root of 39r
c A LaTex expression showing {r} to the power of 2 square root of 39 - rsquare root of 39 + rsquare root of 39r - square root of 39r
d A LaTex expression showing 5{r} to the power of 2 square root of 39 - rsquare root of 39 + 2rsquare root of 39r
e A LaTex expression showing 2{r} to the power of 2 square root of 39 - rsquare root of 39 + rsquare root of 39r - square root of 39r
2
Multiply the radical expressions and simplify the answer
A LaTex expression showing (xsquare root of 3x + square root of 5) times (square root of 5x - {x} to the power of 2 square root of 3)
a A LaTex expression showing {x} to the power of 2 square root of 15 + 3{x} to the power of 3 square root of x + square root of x - {x} to the power of 4 square root of 15
b A LaTex expression showing {x} to the power of 3 square root of 15 - 3{x} to the power of 5 square root of x + 5square root of x + {x} to the power of 2 square root of 15
c A LaTex expression showing 3xsquare root of x + 5
d A LaTex expression showing xsquare root of 15 - 3{x} to the power of 3 square root of x + 5square root of x + {x} to the power of 2 square root of 15
e A LaTex expression showing 3{x} to the power of 3 square root of x + 5square root of x
3
Multiply the radical expressions and simplify the answer
A LaTex expression showing (csquare root of 11 - square root of 2) times ({c} to the power of 2 square root of 2 + csquare root of 11)
a A LaTex expression showing {c} to the power of 3 square root of 22 + 9{c} to the power of 2 - csquare root of 22
b A LaTex expression showing {c} to the power of 3 square root of 22 + 11{c} to the power of 2 - {c} to the power of 2 square root of 2 - csquare root of 22
c A LaTex expression showing 2csquare root of 22 - 11c - 2{c} to the power of 2
d A LaTex expression showing {c} to the power of 3 square root of 22 + 11{c} to the power of 4 - 2{c} to the power of 2 - csquare root of 22
e A LaTex expression showing {c} to the power of 3 square root of 22 + 42{c} to the power of 2 - csquare root of 22
4
Multiply the radical expressions and simplify the answer
A LaTex expression showing (square root of 2 + {x} to the power of 2 square root of 5) times (xsquare root of 2 + square root of 3)
a A LaTex expression showing 2{x} to the power of 2 + {x} to the power of 3 square root of 10 + square root of 6 + {x} to the power of 2 square root of 15
b A LaTex expression showing 2x + {x} to the power of 3 square root of 10 + square root of 6 + {x} to the power of 2 square root of 15
c A LaTex expression showing 2x + 3{x} to the power of 3 square root of 10 + square root of 6 - {x} to the power of 2 square root of 15
d A LaTex expression showing 2x + {x} to the power of 4 square root of 10 + square root of 6 + {x} to the power of 3 square root of 15
e A LaTex expression showing 2x + {x} to the power of 3 square root of 10 + square root of 6 + {x} to the power of 4 square root of 15
5
A LaTex expression showing (square root of 2 + nsquare root of 11) times (square root of 11n + nsquare root of 2n)
Multiply the radical expressions and simplify the answer
a A LaTex expression showing square root of 22n + 13nsquare root of n + {n} to the power of 2 square root of 22n
b A LaTex expression showing square root of n + 13nsquare root of n + {n} to the power of 3 square root of 22n
c A LaTex expression showing square root of 22n - 2nsquare root of n + 11{n} to the power of 2 square root of n + {n} to the power of 2 square root of 22{n to the power of -1 }
d A LaTex expression showing square root of 22n + 2{n} to the power of 3 square root of n - 11nsquare root of n + {n} to the power of 2 square root of 22n
e A LaTex expression showing square root of 22n + 2{n} to the power of 2 + 11nsquare root of n + {n} to the power of 2 square root of 22n
6
A LaTex expression showing (msquare root of 5 - {m} to the power of 2 square root of 7) times (square root of 11m + msquare root of 2m)
Multiply the radical expressions and simplify the answer
a A LaTex expression showing {m} to the power of 2 square root of 55m + {m} to the power of 2 square root of 10m - {m} to the power of 2 square root of 77m + {m} to the power of 3 square root of 14
b A LaTex expression showing msquare root of 55m + {m} to the power of 2 square root of 10m - {m} to the power of 2 square root of 77m - {m} to the power of 3 square root of 14m
c A LaTex expression showing msquare root of 55 + {m} to the power of 2 square root of 10m - {m} to the power of 3 square root of 77m - {m} to the power of 3 square root of 14m
d A LaTex expression showing msquare root of 55m + {m} to the power of 2 square root of 10m - {m} to the power of 2 square root of 77m - 5{m} to the power of 3 square root of 14m
e A LaTex expression showing msquare root of 55m + {m} to the power of 2 square root of 10m + {m} to the power of 4 square root of 77m - {m} to the power of 4 square root of 14m
7
Multiply the radical expressions and simplify the answer
A LaTex expression showing (bsquare root of 7 + square root of 5) times (square root of 3b + square root of 5b)
a A LaTex expression showing bsquare root of 21{b to the power of -1 } + 6square root of b + bsquare root of 35b
b A LaTex expression showing bsquare root of 21b + square root of 15b + bsquare root of 35b + 5square root of b
c A LaTex expression showing bsquare root of 21b + square root of 15b + {b} to the power of -1 square root of 35b + square root of b
d A LaTex expression showing {b} to the power of 2 square root of 21b + square root of 15b + {b} to the power of 3 square root of 35b - 5square root of b
e A LaTex expression showing square root of 21b - square root of 15b + bsquare root of 35 + 5square root of b
Radicals - Multiplying Binomials (Values and Variables) (Level 2) - Mobius Math