Adding and Subtracting from Simplified (Values and Variables) (Level 4)

This math topic focuses on the skills of adding and subtracting radicals that include both numerical and algebraic expressions. The questions involve operations with square roots and cube roots, integrating variables and exponents into the expressions. The complexity of the problems ranges from basic manipulation of similar radicals to more complicated scenarios involving different indices and mixed terms. Each question provides multiple-choice answers, allowing learners to practice and verify their understanding of radical operations in algebra.

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 3xc3-th root of 5x + 2x3-th root of 5x{c to the power of 2 } + 3c3-th root of 5{x to the power of 2 }
a A LaTex expression showing {x} to the power of 2 c3-th root of 6x + {x} to the power of 2 3-th root of 8x{c to the power of 3 } + 5{c} to the power of 2 3-th root of 2{x to the power of 3 }
b A LaTex expression showing 3xc3-th root of 5x + 2x3-th root of 5x{c to the power of 2 } + 3c3-th root of 5{x to the power of 2 }
c A LaTex expression showing xc3-th root of 4{x to the power of 3 } + x3-th root of 6{x to the power of 2 c} + 2{c} to the power of 2 3-th root of 8x
d A LaTex expression showing xc3-th root of 8x + 4x3-th root of 4{x to the power of 2 {c} to the power of 4 } + {c} to the power of 2 3-th root of 8{x to the power of 3 }
2
Add or subtract the radical expressions
A LaTex expression showing 33-th root of 5n + 3p3-th root of 5{n to the power of 2 } - 43-th root of 5p
a A LaTex expression showing 63-th root of 2n + 3{p} to the power of 3 3-th root of 4n - 3-th root of {p to the power of 2 }
b A LaTex expression showing 53-th root of 6{n to the power of 2 } + {p} to the power of 2 3-th root of 3{n to the power of 2 } - 23-th root of p
c A LaTex expression showing 33-th root of 5n + 3p3-th root of 5{n to the power of 2 } - 43-th root of 5p
3
A LaTex expression showing 3rz3-th root of 11 + 4rz3-th root of 11z + 2rz3-th root of 11r
Add or subtract the radical expressions
a A LaTex expression showing {r} to the power of 2 z3-th root of 8 + 3rz3-th root of 9{z to the power of 2 } + 3{r} to the power of 2 z3-th root of 10{r to the power of 2 }
b A LaTex expression showing 3rz3-th root of 11 + 4rz3-th root of 11z + 2rz3-th root of 11r
c A LaTex expression showing {r} to the power of 2 z3-th root of 12 + 5{r} to the power of 2 {z} to the power of 3 3-th root of 13z + rz3-th root of 10{r to the power of 3 }
d A LaTex expression showing 5{r} to the power of 2 z3-th root of 10 + 2r{z} to the power of 3 3-th root of 12z + 3r{z} to the power of 3 3-th root of 14{r to the power of 3 }
4
Add or subtract the radical expressions
A LaTex expression showing 23-th root of 2{n to the power of 2 r} + 3n3-th root of 2{r to the power of 2 } - 4nr3-th root of 2
a A LaTex expression showing 3-th root of {n to the power of 4 {r} to the power of 3 } + {n} to the power of 2 3-th root of {r to the power of 4 } - 5{n} to the power of 2 {r} to the power of 2
b A LaTex expression showing 23-th root of 2{n to the power of 2 r} + 3n3-th root of 2{r to the power of 2 } - 4nr3-th root of 2
c A LaTex expression showing 43-th root of nr + {n} to the power of 3 3-th root of 2{r to the power of 4 } - 3{n} to the power of 2 r3-th root of 5
d A LaTex expression showing 3-th root of 4{n to the power of 2 {r} to the power of 3 } + 4n3-th root of 5r - n{r} to the power of 3
5
Add or subtract the radical expressions
A LaTex expression showing 5ysquare root of 11b + 2square root of 11b - 3bsquare root of 11b
a A LaTex expression showing 5ysquare root of 11b + 2square root of 11b - 3bsquare root of 11b
b A LaTex expression showing 7ysquare root of 9b + square root of 13{b to the power of 2 } - 4bsquare root of 8b
c A LaTex expression showing 5{y} to the power of 3 square root of 12b + square root of 14{b to the power of 3 } - bsquare root of 12{b to the power of 2 }
6
A LaTex expression showing 4b3-th root of 11 - 3mb3-th root of 11 + 4m3-th root of 11m{b to the power of 2 }
Add or subtract the radical expressions
a A LaTex expression showing 3b3-th root of 9 - mb3-th root of 10 + 7m3-th root of 13{m to the power of 2 {b} to the power of 2 }
b A LaTex expression showing 4b3-th root of 11 - 3mb3-th root of 11 + 4m3-th root of 11m{b to the power of 2 }
c A LaTex expression showing b3-th root of 8 - 5{m} to the power of 2 {b} to the power of 3 3-th root of 7 + m3-th root of 14mb
d A LaTex expression showing 3b3-th root of 9 - {m} to the power of 3 b3-th root of 7 + 4{m} to the power of 3 3-th root of 11mb
7
Add or subtract the radical expressions
A LaTex expression showing 43-th root of 5{z to the power of 2 } + 4z3-th root of 5 + 2z3-th root of 5rz
a A LaTex expression showing 43-th root of 5{z to the power of 2 } + 4z3-th root of 5 + 2z3-th root of 5rz
b A LaTex expression showing 33-th root of 8z + 7z3-th root of 2 + 3z3-th root of 8{r to the power of 2 {z} to the power of 3 }
8
Add or subtract the radical expressions
A LaTex expression showing 43-th root of 5{d to the power of 2 {n} to the power of 2 } - 43-th root of 5n + 3d3-th root of 5
a A LaTex expression showing 53-th root of 4dn - 53-th root of 7n + 6{d} to the power of 2 3-th root of 5
b A LaTex expression showing 43-th root of 5{d to the power of 2 {n} to the power of 2 } - 43-th root of 5n + 3d3-th root of 5
c A LaTex expression showing 3-th root of {d to the power of 2 {n} to the power of 3 } - 33-th root of 6n + {d} to the power of 3