Adding and Subtracting (Values and Variables) (Level 2)

This math topic focuses on adding and subtracting radicals that involve both numerical values and variables. The skills practiced involve simplifying radical expressions before performing addition or subtraction. Problems include working with different powers of variables under square roots, and combining like terms to reach a simplified result. Each question presents multiple choices for answers, challenging the learner to identify the correct simplified form of complex radical expressions. These problems help reinforce understanding of basic radical properties, manipulation for simplification, and combining radical terms effectively.

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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Math worksheet on 'Radicals - Adding and Subtracting (Values and Variables) (Level 2)'. 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 11{x to the power of 3 } - square root of 176
a A LaTex expression showing xsquare root of 11x - 4square root of 11
b A LaTex expression showing xsquare root of 10x - 6square root of 8
c A LaTex expression showing 3{x} to the power of 3 square root of 9x - 6square root of 11
d A LaTex expression showing 4xsquare root of 7x - square root of 14
2
Simplify, then add or subtract the radical expressions
A LaTex expression showing square root of 18z + square root of 2
a A LaTex expression showing 3square root of 2z + square root of 2
b A LaTex expression showing square root of z + 1
c A LaTex expression showing square root of 3z + 1
3
Simplify, then add or subtract the radical expressions
A LaTex expression showing square root of 11{b to the power of 2 } + square root of 99b
a A LaTex expression showing bsquare root of 14 + 3square root of 14{b to the power of 3 }
b A LaTex expression showing bsquare root of 11 + 3square root of 11b
c A LaTex expression showing 3bsquare root of 11 + 2square root of 11b
4
Simplify, then add or subtract the radical expressions
A LaTex expression showing square root of 50{c to the power of 3 } + square root of 2{c to the power of 4 }
a A LaTex expression showing csquare root of 4{c to the power of 3 } + 2csquare root of 5
b A LaTex expression showing 2{c} to the power of 2 square root of 2{c to the power of 2 } + {c} to the power of 4 square root of 5
c A LaTex expression showing 2csquare root of 2{c to the power of 3 } + c
d A LaTex expression showing 5csquare root of 2c + {c} to the power of 2 square root of 2
e A LaTex expression showing 2csquare root of 2c + {c} to the power of 3 square root of 4
5
Simplify, then add or subtract the radical expressions
A LaTex expression showing square root of 2 - square root of 8
a A LaTex expression showing square root of 3 - 2
b A LaTex expression showing -1square root of 2
c A LaTex expression showing 3square root of 2
d A LaTex expression showing 5square root of 2
6
Simplify, then add or subtract the radical expressions
A LaTex expression showing square root of 28m + square root of 7
a A LaTex expression showing 2square root of 6m + 3square root of 6
b A LaTex expression showing square root of 5{m to the power of 2 } + 3square root of 6
c A LaTex expression showing 5square root of 4{m to the power of 2 } + square root of 6
d A LaTex expression showing 2square root of 7m + square root of 7
e A LaTex expression showing 3square root of 4m + square root of 8
7
A LaTex expression showing square root of 8m + square root of 2
Simplify, then add or subtract the radical expressions
a A LaTex expression showing 5square root of {m to the power of 3 } + 1
b A LaTex expression showing 2square root of 2m + square root of 2