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Radicals - 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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Multiplying Monomials with 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

b2y13y⋅(b2y7y−4by23){b}^{2}y\sqrt{13y} \cdot ({b}^{2}y\sqrt{7y} - 4b{y}^{2}\sqrt{3})

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 square root of 3d times (3square root of 2 + square root of 5md)
a A LaTex expression showing square root of 6d + dsquare root of 15m
b A LaTex expression showing 3square root of 6d + {d} to the power of 2 square root of 15m
c A LaTex expression showing 3square root of 6d + dsquare root of 15m
d A LaTex expression showing 3square root of d + dsquare root of 15m
e A LaTex expression showing 3square root of 6d + 2dsquare root of m
f A LaTex expression showing 3dsquare root of 6d + dsquare root of 15m
2
Multiply the radical expressions and simplify the answer
A LaTex expression showing ({b} to the power of 2 square root of 3x - 4square root of 7) times {x} to the power of 2 bsquare root of 3b
a A LaTex expression showing 3{x} to the power of 2 {b} to the power of 3 square root of bx - 4{x} to the power of 2 bsquare root of 21b
b A LaTex expression showing 3{x} to the power of 2 {b} to the power of 3 square root of bx - 4bsquare root of 21b
c A LaTex expression showing 15{x} to the power of 2 {b} to the power of 3 square root of bx - 4{x} to the power of 2 bsquare root of 21b
d A LaTex expression showing 3{x} to the power of 2 {b} to the power of 3 square root of bx - 4{x} to the power of 2 {b} to the power of 2 square root of 21
e A LaTex expression showing 3{x} to the power of 2 {b} to the power of 3 square root of bx - 4{x} to the power of 2 bsquare root of 21
f A LaTex expression showing 3{x} to the power of 2 {b} to the power of 3 square root of bx - 4{x} to the power of 2 bsquare root of 21{b to the power of -1 }
3
Multiply the radical expressions and simplify the answer
A LaTex expression showing rsquare root of 3n times (square root of 11r - 3square root of 3)
a A LaTex expression showing {r} to the power of 2 square root of 33n - 9rsquare root of n
b A LaTex expression showing rsquare root of 33nr - 9rsquare root of n
c A LaTex expression showing rnsquare root of 33r - 9rsquare root of n
d A LaTex expression showing {r} to the power of 2 square root of 33nr - 9rsquare root of n
e A LaTex expression showing rsquare root of 33nr - 9rn
f A LaTex expression showing rnsquare root of 33nr - 9rsquare root of n
4
Multiply the radical expressions and simplify the answer
A LaTex expression showing (5{y} to the power of 2 {c} to the power of 2 square root of 7 - ysquare root of 2yc) times {c} to the power of 2 square root of 11y
a A LaTex expression showing 5{c} to the power of 4 {y} to the power of 2 square root of 77y - {c} to the power of 2 ysquare root of 22c
b A LaTex expression showing 5{c} to the power of 4 {y} to the power of 3 square root of 77y - {c} to the power of 2 {y} to the power of 2 square root of 22c
c A LaTex expression showing 5{c} to the power of 4 {y} to the power of 2 square root of 77y - {c} to the power of 2 {y} to the power of 2 square root of 22yc
d A LaTex expression showing 5{c} to the power of 4 {y} to the power of 2 square root of 77y - {c} to the power of 3 {y} to the power of 2 square root of 22
e A LaTex expression showing 5{c} to the power of 4 {y} to the power of 2 square root of 77y - {y} to the power of 2 square root of 22c
f A LaTex expression showing 5{c} to the power of 4 {y} to the power of 2 square root of 77y - {c} to the power of 2 {y} to the power of 2 square root of 22c
5
Multiply the radical expressions and simplify the answer
A LaTex expression showing (5psquare root of 3p + psquare root of 11) times psquare root of 13p
a A LaTex expression showing 5{p} to the power of 4 square root of 39 + {p} to the power of 2 square root of 143p
b A LaTex expression showing 5{p} to the power of 3 square root of 39 + {p} to the power of 2 square root of 143
c A LaTex expression showing 5{p} to the power of 3 square root of 39 + psquare root of 143p
d A LaTex expression showing 5{p} to the power of 3 square root of 39 + {p} to the power of 2 square root of 143{p to the power of -1 }
e A LaTex expression showing 5{p} to the power of 5 square root of 39 + {p} to the power of 2 square root of 143p
f A LaTex expression showing 5{p} to the power of 3 square root of 39 + {p} to the power of 2 square root of 143p
6
Multiply the radical expressions and simplify the answer
A LaTex expression showing square root of 3 times (2square root of 3z - zsquare root of 11zy)
a A LaTex expression showing 6square root of z - zsquare root of 33zy
b A LaTex expression showing 6zsquare root of z - zsquare root of 33zy
c A LaTex expression showing 6square root of z - zsquare root of 33{z to the power of -1 y}
d A LaTex expression showing 6square root of z - zsquare root of 33y
e A LaTex expression showing 3square root of z - zsquare root of 33zy
f A LaTex expression showing 6square root of z - {z} to the power of 2 square root of 33y
7
Multiply the radical expressions and simplify the answer
A LaTex expression showing nsquare root of 11zn times (4znsquare root of 3n + nsquare root of 7zn)
a A LaTex expression showing 4{n} to the power of 2 zsquare root of 33zn + {n} to the power of 3 zsquare root of 77
b A LaTex expression showing 4{n} to the power of 4 zsquare root of 33z + {n} to the power of 3 zsquare root of 77
c A LaTex expression showing 4{n} to the power of 3 zsquare root of 3z + {n} to the power of 3 zsquare root of 77
d A LaTex expression showing 4{n} to the power of 3 zsquare root of 33z + {n} to the power of 3 zsquare root of 77
e A LaTex expression showing 4{n} to the power of 5 zsquare root of 33z + {n} to the power of 3 zsquare root of 77
f A LaTex expression showing 4{n} to the power of 3 zsquare root of 33z + 3{n} to the power of 3 zsquare root of 77