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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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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

27z4−12z4c4−27zc3\sqrt{27{z}^{4}} - \sqrt{12{z}^{4}{c}^{4}} - \sqrt{27z{c}^{3}}

Radicals - Adding and Subtracting (Values and Variables) Worksheet

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Math worksheet on 'Radicals - Adding and Subtracting (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
Simplify, then add or subtract the radical expressions
A LaTex expression showing square root of 175{m to the power of 2 } + square root of 63{m to the power of 2 } - square root of 175{m to the power of 3 c}
a A LaTex expression showing msquare root of 7 + 5msquare root of 7mc
b A LaTex expression showing 8msquare root of 7 + 5msquare root of 7mc
c A LaTex expression showing 8{m} to the power of -1 square root of 7 + 5msquare root of 7mc
d A LaTex expression showing 3msquare root of 4 + 6{m} to the power of 3 square root of 7 - msquare root of 6{m to the power of 3 c}
e A LaTex expression showing 6{m} to the power of 3 square root of 3 + 3{m} to the power of 2 square root of 7 - 6msquare root of 5{m to the power of 2 c}
f A LaTex expression showing 5msquare root of 7 + 5msquare root of 7mc
2
A LaTex expression showing 3-th root of 704{m to the power of 4 } + 3-th root of 297{r to the power of 4 {m} to the power of 4 } - 3-th root of 88{r to the power of 4 {m} to the power of 3 }
Simplify, then add or subtract the radical expressions
a A LaTex expression showing 2m3-th root of 11m + {r} to the power of 3 m3-th root of 7rm - 3rm3-th root of 10r
b A LaTex expression showing 4m3-th root of 14m + 4{r} to the power of 3 {m} to the power of 2 3-th root of 11r{m to the power of 3 } - {r} to the power of 2 {m} to the power of 2 3-th root of 9r
c A LaTex expression showing 4m3-th root of 11m + 3rm3-th root of 11rm - 2rm3-th root of 11r
d A LaTex expression showing {m} to the power of 3 3-th root of 9m + 5rm3-th root of 14rm - r{m} to the power of 2 3-th root of 14r
e A LaTex expression showing 3m3-th root of 10m + 6{r} to the power of 2 m3-th root of 14rm - {r} to the power of 3 {m} to the power of 2 3-th root of 10{r to the power of 2 }
f A LaTex expression showing 3{m} to the power of 3 3-th root of 10{m to the power of 3 } + rm3-th root of 7r{m to the power of 3 } - {r} to the power of 2 m3-th root of 14r
3
Simplify, then add or subtract the radical expressions
A LaTex expression showing 3-th root of 16{r to the power of 2 m} + 3-th root of 54r{m to the power of 4 } - 3-th root of 54{r to the power of 3 {m} to the power of 2 }
a A LaTex expression showing 23-th root of {r to the power of 2 m} + 4m3-th root of 2rm - {r} to the power of 3 3-th root of 5{m to the power of 3 }
b A LaTex expression showing 33-th root of 4{r to the power of 3 m} + m3-th root of r{m to the power of 2 } - r3-th root of m
c A LaTex expression showing 23-th root of 2{r to the power of 2 m} + 3m3-th root of 2rm - 3r3-th root of 2{m to the power of 2 }
d A LaTex expression showing 23-th root of 5{r to the power of 3 m} + 2m3-th root of 5rm - {r} to the power of 3 3-th root of 2m
e A LaTex expression showing 53-th root of {r to the power of 3 {m} to the power of 3 } + 2{m} to the power of 2 3-th root of r{m to the power of 3 } - r3-th root of m
4
Simplify, then add or subtract the radical expressions
A LaTex expression showing square root of 18 + square root of 18{z to the power of 2 {p} to the power of 3 } + square root of 32{p to the power of 4 }
a A LaTex expression showing 3square root of 2 + 3zpsquare root of 2p + 4{p} to the power of 2 square root of 2
b A LaTex expression showing square root of 5 + 5{z} to the power of 2 psquare root of p + psquare root of 2
c A LaTex expression showing 1 + 5zpsquare root of p + {p} to the power of 2
d A LaTex expression showing 5 + 5zpsquare root of {p to the power of 2 } + 6p
e A LaTex expression showing 6 + 6zpsquare root of 5{p to the power of 2 } + 3psquare root of 3
f A LaTex expression showing 3 + 2zpsquare root of p + 3{p} to the power of 3 square root of 3
5
Simplify, then add or subtract the radical expressions
A LaTex expression showing square root of 63c - square root of 28{c to the power of 2 {z} to the power of 2 } + square root of 112{c to the power of 2 {z} to the power of 3 }
a A LaTex expression showing 2square root of 10c - 5{c} to the power of 2 zsquare root of 5 + {c} to the power of 3 zsquare root of 6z
b A LaTex expression showing square root of 6c - {c} to the power of 3 zsquare root of 9 + 4c{z} to the power of 3 square root of 8z
c A LaTex expression showing 3square root of 7c - c{z} to the power of 2 square root of 6 + 4czsquare root of 10{z to the power of 2 }
d A LaTex expression showing 3square root of 7c - 2czsquare root of 7 + 4czsquare root of 7z
e A LaTex expression showing square root of 8{c to the power of 2 } - czsquare root of 6 + 4c{z} to the power of 2 square root of 10z
f A LaTex expression showing 3square root of 5{c to the power of 2 } - czsquare root of 10 + 3{c} to the power of 2 {z} to the power of 2 square root of 9z
6
A LaTex expression showing 3-th root of 81{x to the power of 3 {n} to the power of 4 } - 3-th root of 192x{n to the power of 2 } + 3-th root of 24{x to the power of 4 {n} to the power of 3 }
Simplify, then add or subtract the radical expressions
a A LaTex expression showing 3x{n} to the power of 2 3-th root of 2{n to the power of 3 } - 63-th root of 2x{n to the power of 4 } + x{n} to the power of 2 3-th root of 2x
b A LaTex expression showing {x} to the power of 3 {n} to the power of 3 3-th root of n - 43-th root of 6{x to the power of 3 n} + 2{x} to the power of 2 {n} to the power of 3 3-th root of {x to the power of 2 }
c A LaTex expression showing 3xn3-th root of 3n - 43-th root of 3x{n to the power of 2 } + 2xn3-th root of 3x
d A LaTex expression showing 5x{n} to the power of 3 3-th root of 6{n to the power of 3 } - 43-th root of 5x{n to the power of 2 } + x{n} to the power of 3 3-th root of 6{x to the power of 2 }
e A LaTex expression showing x{n} to the power of 3 3-th root of {n to the power of 3 } - 23-th root of x{n to the power of 3 } + 5{x} to the power of 2 {n} to the power of 2 3-th root of 2x
f A LaTex expression showing xn3-th root of n - 33-th root of xn + xn3-th root of 2x
7
A LaTex expression showing 3-th root of 448{p to the power of 3 } + 3-th root of 189{p to the power of 2 {x} to the power of 3 } - 3-th root of 56{p to the power of 2 {x} to the power of 3 }
Simplify, then add or subtract the radical expressions
a A LaTex expression showing 4p3-th root of 7 + 4x3-th root of 7{p to the power of 2 }
b A LaTex expression showing 7{p} to the power of 3 3-th root of 3 + 2x3-th root of 8p - {x} to the power of 2 3-th root of 7{p to the power of 3 }
c A LaTex expression showing 6p3-th root of 8 + x3-th root of 7p - 2{x} to the power of 3 3-th root of 10{p to the power of 2 }
d A LaTex expression showing 4p3-th root of 7 + 5x3-th root of 7{p to the power of 2 }
e A LaTex expression showing 7{p} to the power of 2 3-th root of 4 + x3-th root of 9{p to the power of 3 } - x3-th root of 8{p to the power of 2 }
f A LaTex expression showing 4p3-th root of 7 + x3-th root of 7{p to the power of 2 }