Multiplying Monomials with Binomials (Values and Variables) (Level 3)

The math topic covers the skills of multiplying monomials with binomials involving radicals and simplifying the results. It involves manipulating expressions that contain variables, constants, and various powers under radical signs, testing one's ability to apply multiplication rules, combine like terms, and simplify radical expressions. This topic is ideal for mastering operations with radicals, particularly focusing on the distributive property and algebraic simplification in the context of radical terms.

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

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Radicals - Multiplying Monomials with Binomials (Values and Variables) Worksheet

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Radicals - Multiplying Monomials with Binomials (Values and Variables)
1
Multiply the radical expressions and simplify the answer
A LaTex expression showing (bsquare root of 11y + 5{b} to the power of 2 square root of 5) times ysquare root of 5y
a A LaTex expression showing {y} to the power of 3 bsquare root of 55 + 25y{b} to the power of 2 square root of y
b A LaTex expression showing {y} to the power of 2 bsquare root of 55 + 25ysquare root of y
c A LaTex expression showing {y} to the power of 2 bsquare root of 55 + 25y{b} to the power of 2 square root of y
d A LaTex expression showing {y} to the power of 2 bsquare root of 55 + 25{y} to the power of 2 {b} to the power of 2 square root of y
2
A LaTex expression showing (3rysquare root of 11ry - {r} to the power of 2 {y} to the power of 2 square root of 7) times {y} to the power of 2 square root of 11r
Multiply the radical expressions and simplify the answer
a A LaTex expression showing 33{y} to the power of 3 {r} to the power of 2 square root of y - {y} to the power of 4 {r} to the power of 2 square root of 77r
b A LaTex expression showing 33{y} to the power of 3 {r} to the power of 2 square root of y - {y} to the power of 5 {r} to the power of 2 square root of 77r
c A LaTex expression showing 33{y} to the power of 3 {r} to the power of 2 square root of y - {y} to the power of 4 {r} to the power of 3 square root of 77r
d A LaTex expression showing 33{y} to the power of 3 {r} to the power of 2 square root of y - {y} to the power of 6 {r} to the power of 2 square root of 77r
e A LaTex expression showing 33{y} to the power of 4 {r} to the power of 2 - {y} to the power of 4 {r} to the power of 2 square root of 77r
3
Multiply the radical expressions and simplify the answer
A LaTex expression showing nsquare root of 11 times ({n} to the power of 2 square root of 3 + 2ndsquare root of 11nd)
a A LaTex expression showing {n} to the power of 3 square root of 33 + 22{n} to the power of 2 dsquare root of n{d to the power of -1 }
b A LaTex expression showing {n} to the power of 3 square root of 33 + 22{n} to the power of 2 dsquare root of nd
c A LaTex expression showing nsquare root of 33 + 22{n} to the power of 2 dsquare root of nd
d A LaTex expression showing {n} to the power of 3 square root of 33 + 22{n} to the power of 2 {d} to the power of 2 square root of nd
e A LaTex expression showing {n} to the power of 3 square root of 33 + 11{n} to the power of 2 dsquare root of nd
4
Multiply the radical expressions and simplify the answer
A LaTex expression showing (square root of 7r + 2y{r} to the power of 2 square root of 2y) times {y} to the power of 2 rsquare root of 11r
a A LaTex expression showing {y} to the power of 3 {r} to the power of 2 square root of 77 + 2{y} to the power of 3 {r} to the power of 3 square root of 22ry
b A LaTex expression showing {y} to the power of 2 {r} to the power of 2 square root of 77 + 2{y} to the power of 3 {r} to the power of 3 square root of 22r
c A LaTex expression showing {y} to the power of 2 {r} to the power of 2 square root of 77 + 2{y} to the power of 3 {r} to the power of 3 square root of 22ry
d A LaTex expression showing {y} to the power of 2 rsquare root of 77 + 2{y} to the power of 3 {r} to the power of 3 square root of 22ry
e A LaTex expression showing {y} to the power of 2 {r} to the power of 2 square root of 77 + 2{y} to the power of 3 {r} to the power of 2 square root of 22ry
5
Multiply the radical expressions and simplify the answer
A LaTex expression showing r{d} to the power of 2 square root of 2r times (5dsquare root of 2rd + rsquare root of 7)
a A LaTex expression showing 10r{d} to the power of 3 square root of d + {r} to the power of 2 {d} to the power of 2 square root of 14r
b A LaTex expression showing 10{r} to the power of 2 {d} to the power of 3 square root of d + {r} to the power of 2 {d} to the power of 2 square root of r
c A LaTex expression showing 10{r} to the power of 2 {d} to the power of 3 square root of d + {r} to the power of 2 {d} to the power of 2 square root of 14r
d A LaTex expression showing 10{r} to the power of 2 {d} to the power of 3 square root of d + {r} to the power of 2 {d} to the power of 2 square root of 14
6
Multiply the radical expressions and simplify the answer
A LaTex expression showing bsquare root of 13yb times (3{y} to the power of 2 square root of 11b + square root of 7)
a A LaTex expression showing 3{b} to the power of 2 {y} to the power of 2 square root of 143y + 4bsquare root of 91yb
b A LaTex expression showing 3{b} to the power of 2 {y} to the power of 2 square root of 143y + bysquare root of 91b
c A LaTex expression showing 3{b} to the power of 2 {y} to the power of 2 square root of 143y + bsquare root of 91yb
d A LaTex expression showing 3{b} to the power of 2 {y} to the power of 2 square root of y + bsquare root of 91yb
e A LaTex expression showing 3{b} to the power of 2 {y} to the power of 2 square root of 143y + bsquare root of 91b
7
Multiply the radical expressions and simplify the answer
A LaTex expression showing (2{d} to the power of 2 {n} to the power of 2 square root of 3 + d{n} to the power of 2 square root of 2) times dnsquare root of 5
a A LaTex expression showing 2{d} to the power of 3 {n} to the power of 3 square root of 15 + {n} to the power of 3 square root of 10
b A LaTex expression showing 2{d} to the power of 3 {n} to the power of 3 square root of 15 + {d} to the power of 2 {n} to the power of 3 square root of 10
c A LaTex expression showing 2{d} to the power of 3 {n} to the power of 3 square root of 15 + {d} to the power of 2 {n} to the power of 4 square root of 10
d A LaTex expression showing 2{d} to the power of 3 {n} to the power of 3 square root of 15 + 5{d} to the power of 2 {n} to the power of 3 square root of 10
e A LaTex expression showing 2{d} to the power of 2 {n} to the power of 3 square root of 15 + {d} to the power of 2 {n} to the power of 3 square root of 10
8
A LaTex expression showing mnsquare root of 13mn times (2m{n} to the power of 2 square root of 2m + square root of 7m)
Multiply the radical expressions and simplify the answer
a A LaTex expression showing 2{m} to the power of 3 {n} to the power of 4 square root of 26n + {m} to the power of 2 nsquare root of 91n
b A LaTex expression showing 2m{n} to the power of 3 square root of 26n + {m} to the power of 2 nsquare root of 91n
c A LaTex expression showing 2{m} to the power of 3 {n} to the power of 3 square root of 26n + {m} to the power of 2 nsquare root of 91n
d A LaTex expression showing 2{m} to the power of 4 {n} to the power of 3 square root of 26n + {m} to the power of 2 nsquare root of 91n
e A LaTex expression showing {m} to the power of 3 {n} to the power of 3 square root of 26n + {m} to the power of 2 nsquare root of 91n