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Radicals - Multiplying Monomials with Binomials (Values and Variables) (Level 2)

This math topic focuses on practicing the multiplication of radicals, specifically multiplying monomials with binomials that involve both values and variables. The content is part of a broader introduction to multiplying radical expressions. Learners are presented with problems where they need to multiply different radical expressions and simplify the results, involving steps like distributing the terms and simplifying using radical rules. Various problem sets challenge learners to multiply and simplify expressions such as square roots that include numerical coefficients and variable terms represented in radical form.

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

d2d⋅(d22−3)d\sqrt{2d} \cdot ({d}^{2}\sqrt{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 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 square root of 5 times ({n} to the power of 2 square root of 11 - square root of 3n)
a A LaTex expression showing {n} to the power of 2 square root of 55 - nsquare root of 15
b A LaTex expression showing {n} to the power of 2 square root of 55 - square root of 15n
c A LaTex expression showing square root of 55 - square root of 15n
d A LaTex expression showing {n} to the power of 2 square root of 55 - square root of 2n
e A LaTex expression showing {n} to the power of 2 square root of 55 - nsquare root of 15n
f A LaTex expression showing nsquare root of 55 - square root of 15n
2
Multiply the radical expressions and simplify the answer
A LaTex expression showing nsquare root of 3n times (nsquare root of 13n - square root of 13)
a A LaTex expression showing 5{n} to the power of 3 square root of 39 - nsquare root of 39n
b A LaTex expression showing {n} to the power of 3 square root of 39 - nsquare root of 39n
c A LaTex expression showing {n} to the power of 3 square root of 39 - {n} to the power of 2 square root of 39
d A LaTex expression showing {n} to the power of 3 square root of 39 - nsquare root of n
e A LaTex expression showing {n} to the power of 3 square root of 39 - {n} to the power of 2 square root of 39n
f A LaTex expression showing {n} to the power of 3 - nsquare root of 39n
3
Multiply the radical expressions and simplify the answer
A LaTex expression showing (square root of 7d + square root of 13) times {d} to the power of 2 square root of 2
a A LaTex expression showing {d} to the power of 2 square root of 14d + {d} to the power of 4 square root of 26
b A LaTex expression showing {d} to the power of 2 square root of 14d + square root of 26
c A LaTex expression showing 2{d} to the power of 2 square root of 14d + {d} to the power of 2 square root of 26
d A LaTex expression showing {d} to the power of 2 square root of 14d + {d} to the power of 2 square root of 26
e A LaTex expression showing dsquare root of 14d + {d} to the power of 2 square root of 26
f A LaTex expression showing {d} to the power of 2 square root of d + {d} to the power of 2 square root of 26
4
Multiply the radical expressions and simplify the answer
A LaTex expression showing square root of 5 times (square root of 2 + zsquare root of 11)
a A LaTex expression showing square root of 10 + z
b A LaTex expression showing square root of 10 + {z} to the power of -1 square root of 55
c A LaTex expression showing square root of 10 + zsquare root of 55
d A LaTex expression showing 4square root of 10 + zsquare root of 55
e A LaTex expression showing 1 + zsquare root of 55
f A LaTex expression showing 5square root of 10 + zsquare root of 55
5
Multiply the radical expressions and simplify the answer
A LaTex expression showing nsquare root of 13 times ({n} to the power of 2 square root of 3 + nsquare root of 5)
a A LaTex expression showing {n} to the power of 3 square root of 39 + {n} to the power of 4 square root of 65
b A LaTex expression showing 2{n} to the power of 3 square root of 39 + {n} to the power of 2 square root of 65
c A LaTex expression showing {n} to the power of 3 square root of 39 + square root of 65
d A LaTex expression showing {n} to the power of 2 square root of 39 + {n} to the power of 2 square root of 65
e A LaTex expression showing {n} to the power of 3 + {n} to the power of 2 square root of 65
f A LaTex expression showing {n} to the power of 3 square root of 39 + {n} to the power of 2 square root of 65
6
Multiply the radical expressions and simplify the answer
A LaTex expression showing square root of 2 times (square root of 2 - square root of 5)
a A LaTex expression showing 1 - square root of 10
b A LaTex expression showing 8 - square root of 10
c A LaTex expression showing 1
d A LaTex expression showing square root of 2 - square root of 10
e A LaTex expression showing 2 - square root of 10
f A LaTex expression showing 2 - square root of 3
7
Multiply the radical expressions and simplify the answer
A LaTex expression showing (square root of 13z + zsquare root of 3z) times zsquare root of 2
a A LaTex expression showing {z} to the power of -1 square root of 26z + {z} to the power of 2 square root of 6z
b A LaTex expression showing zsquare root of 26z + {z} to the power of 2 square root of z
c A LaTex expression showing zsquare root of 26 + {z} to the power of 2 square root of 6z
d A LaTex expression showing zsquare root of 26z + {z} to the power of 3 square root of 6z
e A LaTex expression showing {z} to the power of 2 square root of 26z + {z} to the power of 2 square root of 6z
f A LaTex expression showing zsquare root of 26z + {z} to the power of 2 square root of 6z