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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

(xp2xp+5x5x)⋅x2p5(xp\sqrt{2xp} + 5x\sqrt{5x}) \cdot {x}^{2}p\sqrt{5}

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 xbsquare root of 2b times (bsquare root of 11xb - 5xsquare root of 11)
a A LaTex expression showing x{b} to the power of 5 square root of 22x - 5{x} to the power of 2 bsquare root of 22b
b A LaTex expression showing x{b} to the power of 3 square root of 22x - 5{x} to the power of 2 bsquare root of 22b
c A LaTex expression showing x{b} to the power of 3 square root of 22x - 5{x} to the power of 3 bsquare root of 22b
d A LaTex expression showing x{b} to the power of 3 square root of 22x - 5{x} to the power of 2 {b} to the power of 2 square root of 22b
e A LaTex expression showing x{b} to the power of 3 square root of 22x - 5{x} to the power of 2 {b} to the power of 2 square root of 22
f A LaTex expression showing x{b} to the power of 3 square root of 22x - 5{x} to the power of 4 bsquare root of 22b
2
Multiply the radical expressions and simplify the answer
A LaTex expression showing (4npsquare root of 13 - nsquare root of 7np) times {n} to the power of 2 {p} to the power of 2 square root of 7
a A LaTex expression showing 4{n} to the power of 3 {p} to the power of 3 square root of 91 - 7{n} to the power of 3 {p} to the power of 3 square root of np
b A LaTex expression showing 4{n} to the power of 2 {p} to the power of 3 square root of 91 - 7{n} to the power of 3 {p} to the power of 2 square root of np
c A LaTex expression showing {n} to the power of 3 {p} to the power of 3 square root of 91 - 7{n} to the power of 3 {p} to the power of 2 square root of np
d A LaTex expression showing 4{n} to the power of 4 {p} to the power of 3 square root of 91 - 7{n} to the power of 3 {p} to the power of 2 square root of np
e A LaTex expression showing 4{n} to the power of 3 {p} to the power of 4 square root of 91 - 7{n} to the power of 3 {p} to the power of 2 square root of np
f A LaTex expression showing 4{n} to the power of 3 {p} to the power of 3 square root of 91 - 7{n} to the power of 3 {p} to the power of 2 square root of np
3
Multiply the radical expressions and simplify the answer
A LaTex expression showing square root of 2pd times (pdsquare root of 5 + 4pdsquare root of 2)
a A LaTex expression showing pdsquare root of 10pd + 8pdsquare root of {p to the power of -1 d}
b A LaTex expression showing pdsquare root of 10pd + 8{p} to the power of 2 dsquare root of pd
c A LaTex expression showing p{d} to the power of 2 square root of 10p + 8pdsquare root of pd
d A LaTex expression showing {p} to the power of 2 dsquare root of 10pd + 8pdsquare root of pd
e A LaTex expression showing pdsquare root of 10pd + 8pdsquare root of pd
f A LaTex expression showing pdsquare root of 10pd + 2pdsquare root of pd
4
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 3 square root of 39 + {p} to the power of 2 square root of 143{p to the power of -1 }
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 143p
c 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
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
e A LaTex expression showing 5{p} to the power of 3 square root of 39 + psquare root of 143p
f 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
5
Multiply the radical expressions and simplify the answer
A LaTex expression showing square root of 3x times (3nsquare root of 5 - square root of 5xn)
a A LaTex expression showing 3nsquare root of 15x - square root of 15xn
b A LaTex expression showing 3nsquare root of 15x - square root of 15n
c A LaTex expression showing 3nxsquare root of 15 - xsquare root of 15n
d A LaTex expression showing 3nsquare root of 15x - xsquare root of 15n
e A LaTex expression showing 3nsquare root of 15x - xsquare root of 15
f A LaTex expression showing 3nxsquare root of 15x - xsquare root of 15n
6
Multiply the radical expressions and simplify the answer
A LaTex expression showing xsquare root of 3b times (square root of 7 + 4square root of 13bx)
a A LaTex expression showing xsquare root of 21b + 4xbsquare root of 39x
b A LaTex expression showing xsquare root of 21b + 4xbsquare root of 39{x to the power of -1 }
c A LaTex expression showing xsquare root of 21b + 4xsquare root of 39bx
d A LaTex expression showing {x} to the power of 2 square root of 21b + 4xbsquare root of 39x
e A LaTex expression showing xsquare root of 21b + 4xbsquare root of x
f A LaTex expression showing xsquare root of 21b + 4{x} to the power of 2 bsquare root of 39
7
Multiply the radical expressions and simplify the answer
A LaTex expression showing dsquare root of 3d times (4x{d} to the power of 2 square root of 2x + square root of 11)
a A LaTex expression showing 4{d} to the power of 4 xsquare root of 6x + dsquare root of 33d
b A LaTex expression showing 4{d} to the power of 3 xsquare root of 6d{x to the power of -1 } + dsquare root of 33d
c A LaTex expression showing 4{d} to the power of 3 xsquare root of 6dx + dsquare root of 33
d A LaTex expression showing 4{d} to the power of 3 xsquare root of 6dx + dsquare root of 33d
e A LaTex expression showing 4{d} to the power of 3 xsquare root of 6dx + {d} to the power of 2 square root of 33d
f A LaTex expression showing 5{d} to the power of 3 xsquare root of 6dx + dsquare root of 33d