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Radicals - Multiplying Binomials (Values and Variables) (Level 3)

This math topic focuses on the skill of multiplying binomials involving both radicals and variables. Specifically, learners are required to multiply radical expressions, which may include coefficients and variable terms under different radical symbols, then simplify their results. The problems provided include complex expressions with varying degrees and types of radicals paired with algebraic variables, enhancing conceptual understanding and procedural skills in manipulations involving roots and powers. These types of problems are essential for understanding more advanced topics in algebra and precalculus.

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

(px7p+5p211x)â‹…(px5px+3px2)(px\sqrt{7p} + 5{p}^{2}\sqrt{11x}) \cdot (px\sqrt{5px} + 3px\sqrt{2})

Radicals - Multiplying Binomials (Values and Variables) Worksheet

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Math worksheet on 'Radicals - Multiplying Binomials (Values and Variables) (Level 3)'. Part of a broader unit on 'Radicals - Multiplication Intro' Learn online: app.mobius.academy/math/units/radicals_multiplication_intro/
1
A LaTex expression showing (5{c} to the power of 2 square root of 2n - ncsquare root of 5c) times (nsquare root of 3n - 4csquare root of 2c)
Multiply the radical expressions and simplify the answer
a A LaTex expression showing 5{n} to the power of 2 square root of 6 - {n} to the power of 2 csquare root of 15nc + 2{c} to the power of 3 square root of cn - 4{c} to the power of 3 nsquare root of 10
b A LaTex expression showing 5{n} to the power of 4 {c} to the power of 2 square root of 6 + {n} to the power of 2 {c} to the power of 2 square root of 15nc - 40{c} to the power of 3 square root of cn + 4{c} to the power of 3 nsquare root of 10
c A LaTex expression showing 5{n} to the power of 2 {c} to the power of 2 square root of 6 - {n} to the power of 3 csquare root of 15c - 40{c} to the power of 3 square root of cn + {c} to the power of 3 nsquare root of 10
d A LaTex expression showing 5{n} to the power of 2 {c} to the power of 2 square root of 6 - {n} to the power of 2 csquare root of 15nc + 40{c} to the power of 3 square root of cn + 4{c} to the power of 3 n
e A LaTex expression showing 5{n} to the power of 2 {c} to the power of 2 square root of 6 - {n} to the power of 2 csquare root of 15nc + 40{c} to the power of 3 nsquare root of c - 5{c} to the power of 3 nsquare root of 10
f A LaTex expression showing 5{n} to the power of 2 {c} to the power of 2 square root of 6 - {n} to the power of 2 csquare root of 15nc - 40{c} to the power of 3 square root of cn + 4{c} to the power of 3 nsquare root of 10
2
A LaTex expression showing (2rsquare root of 3z + rzsquare root of 11r) times ({z} to the power of 2 square root of 11r - 2rsquare root of 7rz)
Multiply the radical expressions and simplify the answer
a A LaTex expression showing 2rzsquare root of 33z - 4{r} to the power of 2 zsquare root of 21r + 11{r} to the power of 2 {z} to the power of 3 - 2{r} to the power of 3 zsquare root of 77z
b A LaTex expression showing 2{r} to the power of 2 {z} to the power of 2 square root of 33zr + 4{r} to the power of 2 zsquare root of 21{r to the power of -1 } - 11{r} to the power of 2 {z} to the power of 3 - 2{r} to the power of 3 zsquare root of 77z
c A LaTex expression showing {r} to the power of 3 {z} to the power of 2 square root of 33zr + 4{r} to the power of 2 zsquare root of 21r - 11{r} to the power of 2 {z} to the power of 3 - 2{r} to the power of 3 zsquare root of 77z
d A LaTex expression showing 2r{z} to the power of 2 square root of 33zr + 4{r} to the power of 4 zsquare root of 21r + 11{r} to the power of 2 {z} to the power of 3 square root of r - 2{r} to the power of 3 zsquare root of 77z
e A LaTex expression showing 2r{z} to the power of 2 square root of 33zr - 4{r} to the power of 2 zsquare root of 21r + 11{r} to the power of 2 {z} to the power of 3 - 2{r} to the power of 3 zsquare root of 77z
f A LaTex expression showing 2r{z} to the power of 2 square root of 33zr - 4{r} to the power of 2 zsquare root of 21r + 11{r} to the power of 2 {z} to the power of 3 - {r} to the power of 3 zsquare root of 77z
3
A LaTex expression showing (4psquare root of 13p + {p} to the power of 2 square root of 3) times ({p} to the power of 2 square root of 7n + 2{p} to the power of 2 nsquare root of 3n)
Multiply the radical expressions and simplify the answer
a A LaTex expression showing 4{p} to the power of 4 square root of 91np + {p} to the power of 4 square root of 21n + 8{p} to the power of 3 nsquare root of 39np + 6{p} to the power of 4 nsquare root of n
b A LaTex expression showing 4{p} to the power of 5 square root of 91np + {p} to the power of 4 square root of 21n + 8{p} to the power of 3 nsquare root of 39np + 6{p} to the power of 4 {n} to the power of 2 square root of n
c A LaTex expression showing 4psquare root of 91np + {p} to the power of 4 square root of 21n - 8{p} to the power of 4 nsquare root of 39np + 6{p} to the power of 4 nsquare root of n
d A LaTex expression showing 4{p} to the power of 3 square root of 91np + {p} to the power of 4 nsquare root of 21n + 16{p} to the power of 3 nsquare root of np - 6{p} to the power of 4 nsquare root of n
e A LaTex expression showing 4{p} to the power of 3 square root of 91np + {p} to the power of 4 square root of 21n + 8{p} to the power of 3 nsquare root of 39np + 6{p} to the power of 4 nsquare root of n
f A LaTex expression showing 4{p} to the power of 3 nsquare root of 91n{p to the power of -1 } - {p} to the power of 4 square root of 21n + 8{p} to the power of 3 nsquare root of 39np + 6{p} to the power of 4 nsquare root of n
4
A LaTex expression showing (2{z} to the power of 2 square root of 11n + zsquare root of 13n) times (5square root of 2n - nzsquare root of 3n)
Multiply the radical expressions and simplify the answer
a A LaTex expression showing 10nsquare root of 22 + 5{z} to the power of 3 nsquare root of 26 - 2{n} to the power of 2 {z} to the power of 3 square root of 33 - {n} to the power of 2 {z} to the power of 2 square root of 39
b A LaTex expression showing 10{z} to the power of 2 {n} to the power of 2 square root of 22 + 5zsquare root of 26 + 2{n} to the power of 2 {z} to the power of 3 square root of 33 - {n} to the power of 2 {z} to the power of 2 square root of 39
c A LaTex expression showing 10{z} to the power of 2 nsquare root of 22 + 5{z} to the power of 3 nsquare root of 26 - 2n{z} to the power of 3 square root of 33n + {n} to the power of 2 {z} to the power of 2 square root of 39
d A LaTex expression showing 10{z} to the power of 2 nsquare root of 22 + 5znsquare root of 26 - 2{n} to the power of 2 {z} to the power of 3 square root of 33 - {n} to the power of 2 {z} to the power of 2 square root of 39
e A LaTex expression showing 10{z} to the power of 2 nsquare root of 22 - 5znsquare root of 26 - 2{n} to the power of 2 {z} to the power of 3 square root of 33 + {n} to the power of 2 {z} to the power of 2
f A LaTex expression showing 10{z} to the power of 2 nsquare root of 22 + 5znsquare root of 26 - 2{n} to the power of 2 {z} to the power of 3 square root of 33 - {n} to the power of 3 {z} to the power of 2 square root of 39n
5
A LaTex expression showing (4ysquare root of 5n - {y} to the power of 2 square root of 2) times (ynsquare root of 2 + 3y{n} to the power of 2 square root of 2y)
Multiply the radical expressions and simplify the answer
a A LaTex expression showing 4{y} to the power of 2 nsquare root of 10n + 12{y} to the power of 2 {n} to the power of 3 square root of 3y - 2{y} to the power of 3 n + 6{y} to the power of 3 {n} to the power of 2 square root of y
b A LaTex expression showing 4{y} to the power of 2 nsquare root of 10n + 12{y} to the power of 2 {n} to the power of 2 square root of 10ny - 2{y} to the power of 3 n - 6{y} to the power of 3 {n} to the power of 2 square root of y
c A LaTex expression showing 4{y} to the power of 2 nsquare root of 10{n to the power of -1 } + 12{y} to the power of 2 {n} to the power of 2 square root of 10ny - 2{y} to the power of 3 n + 2{y} to the power of 3 {n} to the power of 2 square root of y
d A LaTex expression showing 4{y} to the power of 2 nsquare root of 10n + 12{y} to the power of 2 {n} to the power of 2 square root of 10n{y to the power of -1 } - 2{y} to the power of 3 {n} to the power of 2 + 6{y} to the power of 3 {n} to the power of 2 square root of y
e A LaTex expression showing {y} to the power of 2 nsquare root of 10n - 12{y} to the power of 2 {n} to the power of 2 square root of 10ny + 2{y} to the power of 3 n - 6{y} to the power of 4 {n} to the power of 2
f A LaTex expression showing 4{y} to the power of 2 nsquare root of 10n + 12{y} to the power of 2 {n} to the power of 2 square root of 10y - 2{y} to the power of 3 n + 2{y} to the power of 3 {n} to the power of 2 square root of y
6
A LaTex expression showing (2zdsquare root of 2zd + z{d} to the power of 2 square root of 2z) times ({d} to the power of 2 square root of 13 + 4zsquare root of 2z)
Multiply the radical expressions and simplify the answer
a A LaTex expression showing 2z{d} to the power of 3 square root of 26zd + 16{z} to the power of 3 dsquare root of d + z{d} to the power of 4 square root of 26z + 8{z} to the power of 3 {d} to the power of 2
b A LaTex expression showing 2z{d} to the power of 3 square root of 26zd - 16{z} to the power of 3 square root of d + z{d} to the power of 4 square root of 26z + 8{z} to the power of 3 {d} to the power of 2 square root of z
c A LaTex expression showing z{d} to the power of 3 square root of 26zd + 16zdsquare root of d - z{d} to the power of 4 square root of 26z + 8{z} to the power of 3 {d} to the power of 2
d A LaTex expression showing 2z{d} to the power of 3 square root of 26z + 16{z} to the power of 3 dsquare root of d - z{d} to the power of 4 square root of 26{z to the power of -1 } + 8{z} to the power of 3 {d} to the power of 2
e A LaTex expression showing z{d} to the power of 4 square root of 26z + 6{z} to the power of 3 dsquare root of d - 8{z} to the power of 3 {d} to the power of 2
f A LaTex expression showing 2z{d} to the power of 3 square root of 26zd - 16{z} to the power of 2 dsquare root of zd + z{d} to the power of 4 square root of 26z + 8{z} to the power of 2 {d} to the power of 2
7
A LaTex expression showing (2square root of 3 + {c} to the power of 2 square root of 3n) times (2nsquare root of 11n - csquare root of 7nc)
Multiply the radical expressions and simplify the answer
a A LaTex expression showing 4nsquare root of 33{n to the power of -1 } + 2n{c} to the power of 2 square root of 33n - 2csquare root of 21nc - {c} to the power of 3 nsquare root of 21c
b A LaTex expression showing 4{n} to the power of 2 square root of 33 - 2{n} to the power of 2 {c} to the power of 2 square root of 33 + 2csquare root of 21nc - {c} to the power of 3 nsquare root of 21c
c A LaTex expression showing 4nsquare root of 33 + 2{n} to the power of 2 {c} to the power of 2 square root of 33 - 2{c} to the power of 2 square root of 21nc + {c} to the power of 3 nsquare root of 21c
d A LaTex expression showing 4nsquare root of 33n - 2{n} to the power of 2 {c} to the power of 2 square root of 33 + csquare root of 21c - {c} to the power of 3 nsquare root of 21c
e A LaTex expression showing 4nsquare root of 33n + 2{n} to the power of 2 {c} to the power of 2 square root of 33 - 2csquare root of 21nc + {c} to the power of 3 nsquare root of 21c
f A LaTex expression showing 4nsquare root of 33n + 2{n} to the power of 2 {c} to the power of 2 square root of 33 - 2csquare root of 21nc - {c} to the power of 3 nsquare root of 21c