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Radicals - Adding and Subtracting (Values and Variables) (Level 3)

This math topic focuses on skills related to simplifying and performing operations with radical expressions that include both values and variables. It entails adding and subtracting radicals and requires a good understanding of combining like terms under the radical and proper handling of variable expressions within radicals. The problems are structured to encourage mastery of simplification techniques and learning how to manipulate algebraic expressions involving square roots in preparation for more advanced algebra topics.

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

12c4+27c3\sqrt{12{c}^{4}} + \sqrt{27{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 3)'. 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 18{m to the power of 2 } - square root of 8m
a A LaTex expression showing 5msquare root of 3 - square root of 5{m to the power of 2 }
b A LaTex expression showing 2m - 5square root of 5m
c A LaTex expression showing 3msquare root of 2 - 2square root of 2m
d A LaTex expression showing 3msquare root of 2 - 4square root of 4{m to the power of 3 }
e A LaTex expression showing {m} to the power of 3 - square root of 2m
f A LaTex expression showing {m} to the power of 3 square root of 3 - square root of m
2
Simplify, then add or subtract the radical expressions
A LaTex expression showing square root of 176{y to the power of 4 } + square root of 99{y to the power of 2 }
a A LaTex expression showing 2{y} to the power of 3 square root of 9 + 6ysquare root of 7
b A LaTex expression showing 6{y} to the power of 4 square root of 12 + 2ysquare root of 12
c A LaTex expression showing 2ysquare root of 7 + 5ysquare root of 11
d A LaTex expression showing 3{y} to the power of 2 square root of 10 + 2ysquare root of 11
e A LaTex expression showing 2{y} to the power of 4 square root of 12 + ysquare root of 9
f A LaTex expression showing 4{y} to the power of 2 square root of 11 + 3ysquare root of 11
3
Simplify, then add or subtract the radical expressions
A LaTex expression showing square root of 176{p to the power of 2 } + square root of 275{p to the power of 2 }
a A LaTex expression showing 9{p} to the power of 3 square root of 11
b A LaTex expression showing psquare root of 11 + 6psquare root of 14
c A LaTex expression showing 9square root of 11
d A LaTex expression showing psquare root of 11
e A LaTex expression showing 9{p} to the power of -1 square root of 11
f A LaTex expression showing 9psquare root of 11
4
Simplify, then add or subtract the radical expressions
A LaTex expression showing square root of 8 - square root of 50b
a A LaTex expression showing 2square root of 2 - 5square root of 2b
b A LaTex expression showing 1 - 5square root of b
c A LaTex expression showing 4 - 8square root of 5b
d A LaTex expression showing 1 - 3square root of {b to the power of 2 }
e A LaTex expression showing 3 - 5square root of 4b
f A LaTex expression showing 2square root of 4 - square root of 5b
5
Simplify, then add or subtract the radical expressions
A LaTex expression showing square root of 8d + square root of 32{d to the power of 2 }
a A LaTex expression showing 2square root of 2{d to the power of 3 } + 7dsquare root of 2
b A LaTex expression showing square root of 2d + dsquare root of 4
c A LaTex expression showing square root of d + 5{d} to the power of 2
d A LaTex expression showing square root of 4{d to the power of 3 } + dsquare root of 4
e A LaTex expression showing square root of {d to the power of 2 } + dsquare root of 5
f A LaTex expression showing 2square root of 2d + 4dsquare root of 2
6
Simplify, then add or subtract the radical expressions
A LaTex expression showing square root of 20c + square root of 125{c to the power of 2 }
a A LaTex expression showing 2square root of 5c + 5csquare root of 5
b A LaTex expression showing 3square root of {c to the power of 2 } + 2csquare root of 8
c A LaTex expression showing square root of 7{c to the power of 3 } + 6{c} to the power of 3 square root of 6
d A LaTex expression showing square root of {c to the power of 2 } + {c} to the power of 3 square root of 7
e A LaTex expression showing square root of 2c + 8{c} to the power of 2 square root of 8
f A LaTex expression showing 5square root of 5c + 2csquare root of 3
7
Simplify, then add or subtract the radical expressions
A LaTex expression showing square root of 80{x to the power of 3 } - square root of 125
a A LaTex expression showing 2xsquare root of 7x - 6square root of 4
b A LaTex expression showing {x} to the power of 3 square root of 2{x to the power of 2 } - 4square root of 2
c A LaTex expression showing {x} to the power of 3 square root of 3x - 6square root of 6
d A LaTex expression showing 2xsquare root of 3{x to the power of 3 } - 5square root of 6
e A LaTex expression showing 3{x} to the power of 2 square root of 5{x to the power of 3 } - 8
f A LaTex expression showing 4xsquare root of 5x - 5square root of 5