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Radicals

Adding and Subtracting (Values and Variables) (Level 5)

This math topic focuses on simplifying, adding, and subtracting radical expressions involving values and variables, ranging from square roots to cube roots. Each problem provides expressions with various complexity levels and requires practice in dealing with arithmetic operations involving radicals. The topic is part of a broader unit on the introduction to radicals, aimed at enhancing students' algebraic skills with radical expressions.

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

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Radicals - Adding and Subtracting (Values and Variables) Worksheet

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Radicals - Adding and Subtracting (Values and Variables)
1
Simplify, then add or subtract the radical expressions
A LaTex expression showing square root of 99rp - square root of 99r{p to the power of 3 } + square root of 44{r to the power of 3 {p} to the power of 2 }
a A LaTex expression showing 3square root of 11rp - 3psquare root of 11rp + 2rpsquare root of 11r
b A LaTex expression showing 4square root of 9rp - 5psquare root of 14{r to the power of 2 {p} to the power of 3 } + r{p} to the power of 3 square root of 14{r to the power of 2 }
c A LaTex expression showing 3square root of 7rp - 6psquare root of 7r{p to the power of 3 } + rpsquare root of 10r
2
Simplify, then add or subtract the radical expressions
A LaTex expression showing 3-th root of 135 + 3-th root of 135{n to the power of 3 {c} to the power of 3 } - 3-th root of 320{c to the power of 2 }
a A LaTex expression showing 63-th root of 8 + nc - 53-th root of 8{c to the power of 2 }
b A LaTex expression showing 3-th root of 7 + 3nc3-th root of 7 - 43-th root of {c to the power of 3 }
c A LaTex expression showing 33-th root of 5 + 3nc3-th root of 5 - 43-th root of 5{c to the power of 2 }
3
A LaTex expression showing square root of 28{m to the power of 2 p} - square root of 28{m to the power of 2 {p} to the power of 4 } + square root of 63m{p to the power of 4 }
Simplify, then add or subtract the radical expressions
a A LaTex expression showing 2msquare root of 7p - 2m{p} to the power of 2 square root of 7 + 3{p} to the power of 2 square root of 7m
b A LaTex expression showing msquare root of 10p - mpsquare root of 3 + 5{p} to the power of 4 square root of 6m
c A LaTex expression showing msquare root of 10p - 3m{p} to the power of 4 square root of 8 + 5psquare root of 4{m to the power of 3 }
4
Simplify, then add or subtract the radical expressions
A LaTex expression showing square root of 12{z to the power of 2 } + square root of 75{c to the power of 3 {z} to the power of 3 } - square root of 27{c to the power of 3 }
a A LaTex expression showing 2zsquare root of 3 + 5czsquare root of 3cz - 3csquare root of 3c
b A LaTex expression showing 5{z} to the power of 3 square root of 5 + 4czsquare root of c{z to the power of 2 } - 4csquare root of 4{c to the power of 2 }
c A LaTex expression showing 5{z} to the power of 3 + 6{c} to the power of 2 {z} to the power of 2 square root of {c to the power of 3 {z} to the power of 2 } - {c} to the power of 2 square root of c
5
A LaTex expression showing 3-th root of 704{m to the power of 3 {p} to the power of 3 } + 3-th root of 704{m to the power of 4 } + 3-th root of 297{p to the power of 3 }
Simplify, then add or subtract the radical expressions
a A LaTex expression showing mp3-th root of 13 + 2m3-th root of 14m + p3-th root of 9
b A LaTex expression showing 4mp3-th root of 11 + 4m3-th root of 11m + 3p3-th root of 11
c A LaTex expression showing 5mp3-th root of 13 + {m} to the power of 2 3-th root of 12m + p3-th root of 12
d A LaTex expression showing 6mp3-th root of 8 + 3m3-th root of 14m + 3p3-th root of 11
6
Simplify, then add or subtract the radical expressions
A LaTex expression showing 3-th root of 704r{c to the power of 3 } + 3-th root of 88{r to the power of 3 c} + 3-th root of 88c
a A LaTex expression showing 2{c} to the power of 3 3-th root of 9r + 5r3-th root of 12c + 33-th root of 13{c to the power of 2 }
b A LaTex expression showing 4c3-th root of 11r + 2r3-th root of 11c + 23-th root of 11c
c A LaTex expression showing 7c3-th root of 12r + 3{r} to the power of 3 3-th root of 13{c to the power of 3 } + 3-th root of 13c
7
Simplify, then add or subtract the radical expressions
A LaTex expression showing square root of 45b{x to the power of 3 } - square root of 80bx + square root of 45{b to the power of 4 {x} to the power of 3 }
a A LaTex expression showing xsquare root of 8b{x to the power of 3 } - square root of 3b{x to the power of 3 } + b{x} to the power of 2 square root of 3{x to the power of 3 }
b A LaTex expression showing xsquare root of 6{b to the power of 2 x} - 7square root of 5bx + bxsquare root of 3x
c A LaTex expression showing 3xsquare root of 5bx - 4square root of 5bx + 3{b} to the power of 2 xsquare root of 5x
d A LaTex expression showing 2xsquare root of 4bx - 3square root of 6b{x to the power of 3 } + {b} to the power of 2 xsquare root of 8x
8
Simplify, then add or subtract the radical expressions
A LaTex expression showing square root of 28{p to the power of 4 {y} to the power of 2 } + square root of 63py - square root of 175{p to the power of 3 }
a A LaTex expression showing 2{p} to the power of 2 ysquare root of 7 + 3square root of 7py - 5psquare root of 7p
b A LaTex expression showing {p} to the power of 3 ysquare root of 7 + 4square root of 9p{y to the power of 3 } - 2{p} to the power of 3 square root of 10{p to the power of 2 }
c A LaTex expression showing {p} to the power of 2 ysquare root of 7 + 3square root of 6{p to the power of 3 y} - 6{p} to the power of 2 square root of 3{p to the power of 2 }