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.

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

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Math worksheet on 'Radicals - Multiplying Monomials with 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
Multiply the radical expressions and simplify the answer
A LaTex expression showing (xsquare root of 13 + 3square root of 5y) times ysquare root of 3xy
a A LaTex expression showing yxsquare root of xy + 3{y} to the power of 2 square root of 15x
b A LaTex expression showing yxsquare root of 39xy + 3ysquare root of 15xy
c A LaTex expression showing yxsquare root of 39xy + 3{y} to the power of 2 xsquare root of 15
d A LaTex expression showing yxsquare root of 39xy + 3{y} to the power of 2 square root of 15x
2
Multiply the radical expressions and simplify the answer
A LaTex expression showing ({d} to the power of 2 nsquare root of 5 + 3{d} to the power of 2 square root of 5) times d{n} to the power of 2 square root of 5
a A LaTex expression showing 15{d} to the power of 3 {n} to the power of 3 + 15{d} to the power of 3 {n} to the power of 2
b A LaTex expression showing 20{d} to the power of 3 {n} to the power of 3
c A LaTex expression showing 5{d} to the power of 3 {n} to the power of 3 + 15{d} to the power of 3 {n} to the power of 2
d A LaTex expression showing 20{d} to the power of 3 {n} to the power of 2
e A LaTex expression showing 5{d} to the power of 3 {n} to the power of 3 + 15{d} to the power of 4 {n} to the power of 2
3
Multiply the radical expressions and simplify the answer
A LaTex expression showing prsquare root of 11pr times (3square root of 11r + {p} to the power of 2 {r} to the power of 2 square root of 2)
a A LaTex expression showing 33p{r} to the power of 2 square root of p + {p} to the power of 4 {r} to the power of 3 square root of 22pr
b A LaTex expression showing 33p{r} to the power of 2 square root of p + {p} to the power of 3 {r} to the power of 3 square root of 22p{r to the power of -1 }
c A LaTex expression showing 33p{r} to the power of 2 square root of p + {p} to the power of 3 {r} to the power of 3 square root of 22{p to the power of -1 r}
d A LaTex expression showing 33p{r} to the power of 2 square root of p + {p} to the power of 3 {r} to the power of 3 square root of 22pr
e A LaTex expression showing 33p{r} to the power of 2 square root of p + {p} to the power of 4 {r} to the power of 3 square root of 22r
4
A LaTex expression showing mzsquare root of 2z times (square root of 11z + 2m{z} to the power of 2 square root of 13m)
Multiply the radical expressions and simplify the answer
a A LaTex expression showing m{z} to the power of 2 square root of 22 + 2{m} to the power of 2 {z} to the power of 4 square root of 26zm
b A LaTex expression showing {m} to the power of -1 {z} to the power of 2 square root of 22 + 2{m} to the power of 2 {z} to the power of 3 square root of 26zm
c A LaTex expression showing m{z} to the power of 2 square root of 22 + 2{m} to the power of 2 {z} to the power of 3 square root of 26zm
d A LaTex expression showing msquare root of 22 + 2{m} to the power of 2 {z} to the power of 3 square root of 26zm
e A LaTex expression showing m{z} to the power of 2 + 2{m} to the power of 2 {z} to the power of 3 square root of 26zm
5
Multiply the radical expressions and simplify the answer
A LaTex expression showing (mpsquare root of 2p + 3{p} to the power of 2 square root of 5) times {p} to the power of 2 square root of 3m
a A LaTex expression showing {p} to the power of 3 msquare root of 6m{p to the power of -1 } + 3{p} to the power of 4 square root of 15m
b A LaTex expression showing {p} to the power of 3 msquare root of 6mp + 3{p} to the power of 4 square root of 15m
c A LaTex expression showing {p} to the power of 3 {m} to the power of 2 square root of 6mp + 3{p} to the power of 4 square root of 15m
d A LaTex expression showing {p} to the power of 3 {m} to the power of 3 square root of 6mp + 3{p} to the power of 4 square root of 15m
e A LaTex expression showing pmsquare root of 6mp + 3{p} to the power of 4 square root of 15m
6
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 + {d} to the power of 2 {n} to the power of 4 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 + {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 + 5{d} to the power of 2 {n} to the power of 3 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 + {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
7
A LaTex expression showing (3{m} to the power of 2 {d} to the power of 2 square root of 3 + {m} to the power of 2 dsquare root of 13d) times {d} to the power of 2 square root of 13m
Multiply the radical expressions and simplify the answer
a A LaTex expression showing 3{d} to the power of 4 {m} to the power of 2 square root of 39m + 13{d} to the power of 3 {m} to the power of 2 square root of md
b A LaTex expression showing 3{d} to the power of 4 {m} to the power of 2 square root of 39m + 13{d} to the power of 3 {m} to the power of 2 square root of m{d to the power of -1 }
c A LaTex expression showing 3{d} to the power of 4 {m} to the power of 2 square root of 39m + 13{d} to the power of 4 {m} to the power of 2 square root of m
d A LaTex expression showing 3{d} to the power of 4 square root of 39m + 13{d} to the power of 3 {m} to the power of 2 square root of md
e A LaTex expression showing 3{d} to the power of 4 {m} to the power of 2 square root of m + 13{d} to the power of 3 {m} to the power of 2 square root of md
Radicals - Multiplying Monomials with Binomials (Values and Variables) (Level 3) - Mobius Math