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

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Radicals - Adding and Subtracting from Simplified (Values and Variables)
1
Add or subtract the radical expressions
A LaTex expression showing 4zsquare root of 5yz + 2square root of 5 - 3zsquare root of 5y
a A LaTex expression showing 3{z} to the power of 3 square root of 4{y to the power of 3 z} + square root of 8 - 3zsquare root of 8y
b A LaTex expression showing 4zsquare root of 5yz + 2square root of 5 - 3zsquare root of 5y
c A LaTex expression showing 4zsquare root of 4y{z to the power of 2 } + square root of 6 - {z} to the power of 3 square root of {y to the power of 3 }
d A LaTex expression showing {z} to the power of 2 square root of 7y{z to the power of 2 } + square root of 7 - {z} to the power of 2 square root of 7y
2
A LaTex expression showing 2n3-th root of 11yn + 33-th root of 11n - 4n3-th root of 11yn
Add or subtract the radical expressions
a A LaTex expression showing -2n3-th root of 11y{n to the power of 3 } + 33-th root of 11n
b A LaTex expression showing -2n3-th root of 11yn + 33-th root of 11n
c A LaTex expression showing n3-th root of 11yn + 33-th root of 11n
d A LaTex expression showing -2n3-th root of 11y{n to the power of 2 } + 33-th root of 11n
3
Add or subtract the radical expressions
A LaTex expression showing 2zsquare root of 11zb + 3{z} to the power of 2 bsquare root of 11 - 3bsquare root of 11b
a A LaTex expression showing zsquare root of 12z{b to the power of 2 } + 6zbsquare root of 12 - 5{b} to the power of 3 square root of 8b
b A LaTex expression showing 4{z} to the power of 3 square root of 13{z to the power of 3 b} + 2zbsquare root of 14 - 5bsquare root of 7b
c A LaTex expression showing 2zsquare root of 11zb + 3{z} to the power of 2 bsquare root of 11 - 3bsquare root of 11b
d A LaTex expression showing zsquare root of 14zb + 4{z} to the power of 4 {b} to the power of 3 square root of 11 - 5bsquare root of 8b
e A LaTex expression showing 3{z} to the power of 2 square root of 12zb + {z} to the power of 3 bsquare root of 10 - 6{b} to the power of 3 square root of 9b
4
Add or subtract the radical expressions
A LaTex expression showing 4x{n} to the power of 2 square root of 11x + 5nsquare root of 11xn - 5{x} to the power of 2 nsquare root of 11
a A LaTex expression showing 5x{n} to the power of 2 square root of 13{x to the power of 2 } + 8nsquare root of 14xn - 7{x} to the power of 3 nsquare root of 10
b A LaTex expression showing 4x{n} to the power of 2 square root of 11x + 5nsquare root of 11xn - 5{x} to the power of 2 nsquare root of 11
5
Add or subtract the radical expressions
A LaTex expression showing 2cdsquare root of 5 + 5{d} to the power of 2 square root of 5c + 5square root of 5
a A LaTex expression showing 4{c} to the power of 2 dsquare root of 5 + 4dsquare root of 8{c to the power of 3 } + 5square root of 6
b A LaTex expression showing cdsquare root of 4 + 2dsquare root of c + square root of 5
c A LaTex expression showing {c} to the power of 3 dsquare root of 2 + 7{d} to the power of 4 square root of 3{c to the power of 3 } + 3square root of 7
d A LaTex expression showing 2cdsquare root of 5 + 5{d} to the power of 2 square root of 5c + 5square root of 5
6
Add or subtract the radical expressions
A LaTex expression showing 4bm3-th root of 3 - 4bm3-th root of 3b + 3bm3-th root of 3
a A LaTex expression showing 7bm3-th root of 3 - 4bm3-th root of 3b
b A LaTex expression showing 7{b} to the power of -1 m3-th root of 3 - 4bm3-th root of 3b
c A LaTex expression showing 3b{m} to the power of 3 - b{m} to the power of 2 3-th root of 5b + b{m} to the power of 3 3-th root of 6
d A LaTex expression showing 7{b} to the power of 3 {m} to the power of 3 3-th root of 3 - bm3-th root of b + {b} to the power of 3 m
e A LaTex expression showing 7bm - 4bm3-th root of 3b
7
Add or subtract the radical expressions
A LaTex expression showing 4{r} to the power of 2 square root of 3 + 5rzsquare root of 3z - 5{r} to the power of 2 square root of 3z
a A LaTex expression showing 4{r} to the power of 2 square root of 3 + 5rzsquare root of 3z - 5{r} to the power of 2 square root of 3z
b A LaTex expression showing 3rsquare root of 5 + 7rzsquare root of {z to the power of 2 } - 2rsquare root of 6{z to the power of 3 }
c A LaTex expression showing 2r + 6rzsquare root of {z to the power of 2 } - 7{r} to the power of 4 square root of 6z
8
Add or subtract the radical expressions
A LaTex expression showing 3rsquare root of 5r - 4y{r} to the power of 2 square root of 5y - 4yrsquare root of 5yr
a A LaTex expression showing 3rsquare root of 5r - 4y{r} to the power of 2 square root of 5y - 4yrsquare root of 5yr
b A LaTex expression showing 6{r} to the power of 2 square root of 3r - 7{y} to the power of 2 rsquare root of 3{y to the power of 3 } - 6{y} to the power of 3 rsquare root of 6{y to the power of 3 {r} to the power of 3 }
c A LaTex expression showing {r} to the power of 3 square root of 8{r to the power of 3 } - yrsquare root of y - 4yrsquare root of {y to the power of 2 r}
d A LaTex expression showing 2rsquare root of 2r - 2y{r} to the power of 2 square root of 3{y to the power of 3 } - 3{y} to the power of 2 {r} to the power of 3 square root of 2{y to the power of 3 r}