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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

48r3−27rx2+75r4x\sqrt{48{r}^{3}} - \sqrt{27r{x}^{2}} + \sqrt{75{r}^{4}x}

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 12{n to the power of 4 } - square root of 12{n to the power of 2 } - square root of 27{m to the power of 4 }
a A LaTex expression showing {n} to the power of 3 - 5nsquare root of 3 - {m} to the power of 4
b A LaTex expression showing {n} to the power of 2 - nsquare root of 4 - 3{m} to the power of 4
c A LaTex expression showing 5{n} to the power of 2 - nsquare root of 6 - 6{m} to the power of 2 square root of 2
d A LaTex expression showing {n} to the power of 2 square root of 5 - 5{n} to the power of 2 - {m} to the power of 2 square root of 5
e A LaTex expression showing 2{n} to the power of 2 square root of 3 - 2nsquare root of 3 - 3{m} to the power of 2 square root of 3
f A LaTex expression showing {n} to the power of 2 - 2nsquare root of 4 - 3{m} to the power of 4
2
Simplify, then add or subtract the radical expressions
A LaTex expression showing square root of 175 + square root of 63{y to the power of 4 } + square root of 112{b to the power of 3 }
a A LaTex expression showing 5square root of 7 + 3{y} to the power of 2 square root of 7 + 4bsquare root of 7b
b A LaTex expression showing 5square root of 6 + 2{y} to the power of 2 square root of 4 + bsquare root of 9b
c A LaTex expression showing 7square root of 9 + 5{y} to the power of 3 square root of 6 + 3bsquare root of 8b
d A LaTex expression showing 8square root of 5 + 3ysquare root of 3 + 7bsquare root of 5b
e A LaTex expression showing 4square root of 8 + 3ysquare root of 8 + bsquare root of 7b
f A LaTex expression showing 8square root of 6 + 4{y} to the power of 3 square root of 10 + 3{b} to the power of 2 square root of 8{b to the power of 3 }
3
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 11m + 3rm3-th root of 11rm - 2rm3-th root of 11r
c 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 }
d 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
e 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
f 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
4
Simplify, then add or subtract the radical expressions
A LaTex expression showing square root of 12{d to the power of 2 {b} to the power of 2 } + square root of 48d{b to the power of 3 } - square root of 12{b to the power of 4 }
a A LaTex expression showing 2dbsquare root of 3 + 4bsquare root of 3db - 2{b} to the power of 2 square root of 3
b A LaTex expression showing 4{d} to the power of 3 bsquare root of 6 + {b} to the power of 3 square root of d{b to the power of 3 } - 2bsquare root of 3
c A LaTex expression showing 4dbsquare root of 4 + 4{b} to the power of 2 square root of db - 3b
d A LaTex expression showing 3{d} to the power of 3 b + 7bsquare root of 2db - {b} to the power of 3 square root of 2
e A LaTex expression showing db + 4bsquare root of 2{d to the power of 3 {b} to the power of 2 } - 2b
f A LaTex expression showing 3{d} to the power of 3 bsquare root of 4 + bsquare root of 2d{b to the power of 3 } - {b} to the power of 4 square root of 2
5
A LaTex expression showing square root of 28{y to the power of 3 {b} to the power of 4 } + square root of 175y{b to the power of 3 } + square root of 63{y to the power of 2 b}
Simplify, then add or subtract the radical expressions
a A LaTex expression showing 2y{b} to the power of 2 square root of 7y + 5bsquare root of 7yb + 3ysquare root of 7b
b A LaTex expression showing 5y{b} to the power of 4 square root of 6y + 7{b} to the power of 3 square root of 10yb + 4ysquare root of 7b
c A LaTex expression showing 2ybsquare root of 4{y to the power of 3 } + 6bsquare root of 6{y to the power of 2 {b} to the power of 3 } + {y} to the power of 3 square root of 5{b to the power of 2 }
d A LaTex expression showing y{b} to the power of 4 square root of 9{y to the power of 2 } + bsquare root of 7{y to the power of 2 {b} to the power of 2 } + 4ysquare root of 6b
e A LaTex expression showing 2y{b} to the power of 2 square root of 7y + 6bsquare root of 5{y to the power of 2 b} + ysquare root of 3{b to the power of 3 }
f A LaTex expression showing ybsquare root of 7y + 3bsquare root of 3{y to the power of 2 {b} to the power of 3 } + 2{y} to the power of 3 square root of 5{b to the power of 2 }
6
Simplify, then add or subtract the radical expressions
A LaTex expression showing 3-th root of 320{p to the power of 3 {n} to the power of 3 } - 3-th root of 40 + 3-th root of 320p
a A LaTex expression showing pn3-th root of 8 - 23-th root of 2 + 73-th root of 2p
b A LaTex expression showing pn3-th root of 2 - 3-th root of 3 + 53-th root of 4p
c A LaTex expression showing pn3-th root of 8 - 3-th root of 8 + 3-th root of 8p
d A LaTex expression showing 4pn3-th root of 5 - 23-th root of 5 + 43-th root of 5p
e A LaTex expression showing pn - 3-th root of 8 + 53-th root of 3p
f A LaTex expression showing 3{p} to the power of 2 n - 3-th root of 2 + 63-th root of 8p
7
Simplify, then add or subtract the radical expressions
A LaTex expression showing 3-th root of 24 - 3-th root of 24{r to the power of 3 {y} to the power of 4 } + 3-th root of 81{y to the power of 3 }
a A LaTex expression showing 3 - ry3-th root of y + 4y3-th root of 3
b A LaTex expression showing 3-th root of 2 - {r} to the power of 2 {y} to the power of 2 3-th root of y + y
c A LaTex expression showing 23-th root of 6 - {r} to the power of 3 {y} to the power of 3 3-th root of {y to the power of 2 } + {y} to the power of 2
d A LaTex expression showing 23-th root of 3 - 2ry3-th root of 3y + 3y3-th root of 3
e A LaTex expression showing 3-th root of 6 - r{y} to the power of 3 3-th root of 5{y to the power of 2 } + {y} to the power of 2 3-th root of 6
f A LaTex expression showing 1 - ry3-th root of 3y + 5{y} to the power of 2 3-th root of 3