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Radicals - Adding and Subtracting from Simplified (Values and Variables) (Level 5)

This math topic focuses on practicing how to add and subtract radical expressions that involve both numerical and algebraic values, including roots of different indices and powers of variables. The problems require simplifying and combining terms with similar radical components. Each question presents multiple-choice answers, requiring the student to select or verify the correct simplified form of the given radical expressions. This forms part of a larger introductory unit on addition and subtraction of radicals.

Work on practice problems directly here, or download the printable pdf worksheet to practice offline.

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Adding and Subtracting from Simplified (Values and Variables)

Complete these online problems with 80% or 4 correct answers in a row. Results are immediate.

Add or subtract the radical expressions

35−5x25y+3y5xy3\sqrt{5} - 5{x}^{2}\sqrt{5y} + 3y\sqrt{5xy}

Radicals - Adding and Subtracting from Simplified (Values and Variables) Worksheet

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Math worksheet on 'Radicals - Adding and Subtracting from Simplified (Values and Variables) (Level 5)'. Part of a broader unit on 'Radicals - Addition and Subtraction Intro' Learn online: app.mobius.academy/math/units/radicals_addition_and_subtraction_intro/
1
A LaTex expression showing 2msquare root of 3 + 5mnsquare root of 3m + 3mnsquare root of 3mn
Add or subtract the radical expressions
a A LaTex expression showing 2msquare root of 3 + 5mnsquare root of 3m + 3mnsquare root of 3mn
b A LaTex expression showing 2m + 8m{n} to the power of 2 square root of 2m + 2m{n} to the power of 2 square root of {m to the power of 2 {n} to the power of 2 }
c A LaTex expression showing 3msquare root of 3 + 3mnsquare root of 4m + 4mnsquare root of 3mn
d A LaTex expression showing msquare root of 5 + 4{m} to the power of 3 {n} to the power of 3 square root of m + 3{m} to the power of 3 nsquare root of m{n to the power of 2 }
e A LaTex expression showing msquare root of 2 + 2m{n} to the power of 2 square root of 4m + 5mnsquare root of 5mn
f A LaTex expression showing 3{m} to the power of 2 square root of 3 + 7m{n} to the power of 3 square root of 3m + 2mnsquare root of 5mn
2
Add or subtract the radical expressions
A LaTex expression showing 3psquare root of 3pz - 4{p} to the power of 2 square root of 3z + 5pzsquare root of 3
a A LaTex expression showing 5psquare root of 3{p to the power of 3 {z} to the power of 2 } - 4{p} to the power of 2 square root of {z to the power of 2 } + 2pz
b A LaTex expression showing 4psquare root of {p to the power of 2 z} - 4psquare root of z + 4pzsquare root of 3
c A LaTex expression showing 3psquare root of 3pz - 4{p} to the power of 2 square root of 3z + 5pzsquare root of 3
d A LaTex expression showing 3{p} to the power of 2 square root of pz - 4{p} to the power of 2 square root of 4{z to the power of 2 } + 6{p} to the power of 3 zsquare root of 5
e A LaTex expression showing 5{p} to the power of 2 square root of 3pz - 5psquare root of z + 8p{z} to the power of 2
f A LaTex expression showing 4psquare root of 3pz - 4{p} to the power of 4 square root of z + 4pz
3
Add or subtract the radical expressions
A LaTex expression showing 3c3-th root of 5cd + 2c3-th root of 5 - 33-th root of 5{c to the power of 2 {d} to the power of 2 }
a A LaTex expression showing c3-th root of c{d to the power of 3 } + c3-th root of 3 - 63-th root of 3c{d to the power of 4 }
b A LaTex expression showing 6c3-th root of 5{c to the power of 3 {d} to the power of 3 } + 2{c} to the power of 2 3-th root of 2 - 3-th root of 6{c to the power of 3 d}
c A LaTex expression showing c3-th root of 6{c to the power of 2 d} + 5c3-th root of 2 - 3-th root of 2{c to the power of 3 {d} to the power of 4 }
d A LaTex expression showing 5c3-th root of 4c{d to the power of 2 } + 3c3-th root of 8 - 3-th root of 8{c to the power of 3 d}
e A LaTex expression showing 2{c} to the power of 2 3-th root of 4{c to the power of 2 d} + 2{c} to the power of 2 3-th root of 4 - 53-th root of 3c{d to the power of 2 }
f A LaTex expression showing 3c3-th root of 5cd + 2c3-th root of 5 - 33-th root of 5{c to the power of 2 {d} to the power of 2 }
4
Add or subtract the radical expressions
A LaTex expression showing 4{m} to the power of 2 xsquare root of 2 - 4{x} to the power of 2 square root of 2 - 2msquare root of 2x
a A LaTex expression showing 3mx - 5xsquare root of 2 - 3msquare root of x
b A LaTex expression showing 5{m} to the power of 4 xsquare root of 5 - 3xsquare root of 2 - msquare root of x
c A LaTex expression showing {m} to the power of 4 xsquare root of 5 - {x} to the power of 2 square root of 3 - msquare root of 5x
d A LaTex expression showing 4{m} to the power of 2 xsquare root of 2 - 4{x} to the power of 2 square root of 2 - 2msquare root of 2x
e A LaTex expression showing mxsquare root of 5 - 5{x} to the power of 4 - msquare root of 4x
5
Add or subtract the radical expressions
A LaTex expression showing 4m3-th root of 2my - 33-th root of 2 + 3m3-th root of 2
a A LaTex expression showing 4m3-th root of 2my - 33-th root of 2 + 3m3-th root of 2
b A LaTex expression showing 5{m} to the power of 2 3-th root of my - 1 + 6m3-th root of 4
c A LaTex expression showing {m} to the power of 2 3-th root of 2m{y to the power of 2 } - 3-th root of 4 + 4{m} to the power of 3 3-th root of 3
d A LaTex expression showing {m} to the power of 2 3-th root of {m to the power of 2 {y} to the power of 3 } - 3-th root of 2 + m
6
Add or subtract the radical expressions
A LaTex expression showing 43-th root of 3z + 33-th root of 3z{c to the power of 2 } + 3zc3-th root of 3c
a A LaTex expression showing 43-th root of 3z + 33-th root of 3z{c to the power of 2 } + 3zc3-th root of 3c
b A LaTex expression showing 23-th root of 6{z to the power of 2 } + 33-th root of 6z{c to the power of 2 } + 4z{c} to the power of 2 3-th root of 3c
c A LaTex expression showing 63-th root of 3{z to the power of 2 } + 53-th root of 6zc + 2zc3-th root of 2c
d A LaTex expression showing 53-th root of {z to the power of 2 } + 3-th root of 6{z to the power of 2 {c} to the power of 4 } + 2{z} to the power of 2 c3-th root of 5c
e A LaTex expression showing 63-th root of 4z + 43-th root of 3zc + 6zc3-th root of c
f A LaTex expression showing 3-th root of {z to the power of 2 } + 3-th root of 4z{c to the power of 4 } + 6{z} to the power of 3 c3-th root of 2c
7
Add or subtract the radical expressions
A LaTex expression showing 4d3-th root of 3d{r to the power of 2 } - 23-th root of 3d - 33-th root of 3dr
a A LaTex expression showing 4d3-th root of 3d{r to the power of 2 } - 23-th root of 3d - 33-th root of 3dr
b A LaTex expression showing 3{d} to the power of 2 3-th root of 2dr - 3-th root of 2{d to the power of 3 } - 3-th root of 4dr
c A LaTex expression showing 3{d} to the power of 2 3-th root of 5dr - 33-th root of 2d - 3-th root of dr
d A LaTex expression showing 5d3-th root of d{r to the power of 4 } - 43-th root of 4d - 3-th root of {d to the power of 2 r}
e A LaTex expression showing 7d3-th root of 2d{r to the power of 4 } - 3-th root of {d to the power of 3 } - 63-th root of dr
f A LaTex expression showing 6d3-th root of 5d{r to the power of 2 } - 3-th root of 5d - 3-th root of 5dr