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Radicals - Adding and Subtracting (Values and Variables) (Level 4)

This math topic focuses on the practice of adding and subtracting radicals, specifically covering both radicals involving numerical values and those with variables. Each of the seven questions requires the student to simplify radical expressions, then perform addition or subtraction. The radical expressions vary across different indices and include mixed variables, testing a student's ability to manipulate and simplify under root terms systematically. This is part of introductory learning to radical addition and subtraction.

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

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Adding and Subtracting (Values and Variables)

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

Simplify, then add or subtract the radical expressions

56n4m3+189m43+56n4m33\sqrt[3]{56{n}^{4}m} + \sqrt[3]{189{m}^{4}} + \sqrt[3]{56{n}^{4}{m}^{3}}

Radicals - Adding and Subtracting (Values and Variables) Worksheet

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Math worksheet on 'Radicals - Adding and Subtracting (Values and Variables) (Level 4)'. 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 3-th root of 56{n to the power of 4 m} + 3-th root of 189{m to the power of 4 } + 3-th root of 56{n to the power of 4 {m} to the power of 3 }
Simplify, then add or subtract the radical expressions
a A LaTex expression showing n3-th root of 10nm + {m} to the power of 2 3-th root of 7m + 5nm3-th root of 7n
b A LaTex expression showing n3-th root of 10{n to the power of 2 m} + 3m3-th root of 6m + 5{n} to the power of 3 {m} to the power of 2 3-th root of 5n
c A LaTex expression showing {n} to the power of 2 3-th root of 10{n to the power of 3 {m} to the power of 2 } + 4m3-th root of 5m + 2nm3-th root of 10n
d A LaTex expression showing 4n3-th root of 3n{m to the power of 2 } + 3m3-th root of 6m + n{m} to the power of 3 3-th root of 8n
e A LaTex expression showing 2n3-th root of 7nm + 3m3-th root of 7m + 2nm3-th root of 7n
2
Simplify, then add or subtract the radical expressions
A LaTex expression showing 3-th root of 81y - 3-th root of 192{y to the power of 2 {n} to the power of 2 } - 3-th root of 192{y to the power of 2 {n} to the power of 3 }
a A LaTex expression showing 53-th root of 6{y to the power of 3 } - 23-th root of 2{y to the power of 3 {n} to the power of 4 } - 3n3-th root of {y to the power of 2 }
b A LaTex expression showing 63-th root of {y to the power of 2 } - 53-th root of 5{y to the power of 2 n} - 2{n} to the power of 3 3-th root of 6y
c A LaTex expression showing 3-th root of 3y - 73-th root of y{n to the power of 2 } - 7n3-th root of {y to the power of 3 }
d A LaTex expression showing 33-th root of 3y - 43-th root of 3{y to the power of 2 {n} to the power of 2 } - 4n3-th root of 3{y to the power of 2 }
e A LaTex expression showing 3-th root of 6{y to the power of 3 } - 73-th root of 2{y to the power of 2 n} - 4n3-th root of 6{y to the power of 2 }
3
Simplify, then add or subtract the radical expressions
A LaTex expression showing square root of 20y{z to the power of 2 } - square root of 45y{z to the power of 3 } + square root of 45{y to the power of 4 {z} to the power of 4 }
a A LaTex expression showing zsquare root of 4{y to the power of 3 } - 4{z} to the power of 3 square root of 8{y to the power of 3 {z} to the power of 3 } + 2{y} to the power of 2 {z} to the power of 2 square root of 8
b A LaTex expression showing zsquare root of 8y - 3zsquare root of 8y{z to the power of 3 } + {y} to the power of 3 z
c A LaTex expression showing 2zsquare root of 5y - 3zsquare root of 5yz + 3{y} to the power of 2 {z} to the power of 2 square root of 5
d A LaTex expression showing 3{z} to the power of 2 square root of 2y - 6zsquare root of 7yz + y{z} to the power of 2 square root of 7
e A LaTex expression showing {z} to the power of 3 square root of {y to the power of 3 } - zsquare root of 3yz + 3{y} to the power of 4 {z} to the power of 4 square root of 3
f A LaTex expression showing 5zsquare root of 6{y to the power of 3 } - zsquare root of 5{y to the power of 3 {z} to the power of 2 } + 4{y} to the power of 4 {z} to the power of 3
4
Simplify, then add or subtract the radical expressions
A LaTex expression showing 3-th root of 135r - 3-th root of 40{r to the power of 2 {d} to the power of 3 } + 3-th root of 320r{d to the power of 4 }
a A LaTex expression showing 23-th root of 8{r to the power of 3 } - 2{d} to the power of 2 3-th root of 6{r to the power of 4 } + 7d3-th root of 2rd
b A LaTex expression showing 53-th root of 7r - 4d3-th root of r + {d} to the power of 3 3-th root of 2{r to the power of 2 d}
c A LaTex expression showing 53-th root of r - 3{d} to the power of 2 3-th root of 3{r to the power of 2 } + 7d3-th root of 8rd
d A LaTex expression showing 33-th root of 2{r to the power of 3 } - {d} to the power of 3 3-th root of 7r + 2{d} to the power of 3 3-th root of rd
e A LaTex expression showing 33-th root of 5r - 2d3-th root of 5{r to the power of 2 } + 4d3-th root of 5rd
f A LaTex expression showing 43-th root of 5{r to the power of 3 } - 4{d} to the power of 3 3-th root of r + 2d3-th root of 2{r to the power of 3 d}
5
Simplify, then add or subtract the radical expressions
A LaTex expression showing 3-th root of 40{r to the power of 4 } + 3-th root of 320m - 3-th root of 320{m to the power of 4 {r} to the power of 3 }
a A LaTex expression showing {r} to the power of 2 3-th root of 5r + 73-th root of 4m - 2mr3-th root of 4m
b A LaTex expression showing {r} to the power of 3 3-th root of 5r + 43-th root of 6{m to the power of 2 } - mr3-th root of 8m
c A LaTex expression showing {r} to the power of 2 3-th root of r + 33-th root of 8m - 3{m} to the power of 3 r3-th root of 4m
d A LaTex expression showing 2r3-th root of 5r + 43-th root of 5m - 4mr3-th root of 5m
e A LaTex expression showing 4{r} to the power of 2 3-th root of 3{r to the power of 2 } + 3-th root of 2{m to the power of 3 } - 4{m} to the power of 2 r3-th root of 8m
f A LaTex expression showing 5r3-th root of 2{r to the power of 3 } + 73-th root of 8m - 5mr3-th root of 3{m to the power of 2 }
6
Simplify, then add or subtract the radical expressions
A LaTex expression showing square root of 63{p to the power of 4 {d} to the power of 2 } + square root of 112{p to the power of 2 } - square root of 63{p to the power of 2 {d} to the power of 4 }
a A LaTex expression showing {p} to the power of 4 dsquare root of 6 + 2{p} to the power of 2 square root of 5 - {p} to the power of 3 {d} to the power of 2 square root of 6
b A LaTex expression showing 3{p} to the power of 2 dsquare root of 7 + 4psquare root of 7 - 3p{d} to the power of 2 square root of 7
c A LaTex expression showing 3p{d} to the power of 2 square root of 10 + 3psquare root of 9 - p{d} to the power of 2 square root of 4
d A LaTex expression showing pdsquare root of 5 + 6psquare root of 9 - 4{p} to the power of 2 {d} to the power of 3 square root of 8
e A LaTex expression showing 6{p} to the power of 3 dsquare root of 8 + 2psquare root of 4 - p{d} to the power of 4 square root of 9
f A LaTex expression showing {p} to the power of 2 dsquare root of 10 + 4{p} to the power of 2 square root of 8 - 2{p} to the power of 2 dsquare root of 9
7
Simplify, then add or subtract the radical expressions
A LaTex expression showing square root of 8{b to the power of 3 {y} to the power of 2 } - square root of 32b{y to the power of 4 } - square root of 50b{y to the power of 2 }
a A LaTex expression showing 2bysquare root of 2b - 4{y} to the power of 2 square root of 2b - 5ysquare root of 2b
b A LaTex expression showing {b} to the power of 2 ysquare root of 3b - 6{y} to the power of 2 square root of 2{b to the power of 3 } - 5{y} to the power of 2 square root of 4b
c A LaTex expression showing 4b{y} to the power of 3 square root of {b to the power of 2 } - {y} to the power of 3 square root of 5b - 7ysquare root of b
d A LaTex expression showing bysquare root of b - 5ysquare root of 3{b to the power of 3 } - 5{y} to the power of 2 square root of 2{b to the power of 2 }
e A LaTex expression showing {b} to the power of 2 ysquare root of b - 5ysquare root of {b to the power of 2 } - 6ysquare root of 2b
f A LaTex expression showing {b} to the power of 2 ysquare root of 2{b to the power of 3 } - {y} to the power of 2 square root of {b to the power of 2 } - 8ysquare root of 2b