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Radicals - 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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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

48b2+3b4\sqrt{48{b}^{2}} + \sqrt{3{b}^{4}}

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 18{n to the power of 2 } + square root of 2{n to the power of 4 }
a A LaTex expression showing 3nsquare root of 2 + {n} to the power of 2 square root of 2
b A LaTex expression showing 2n
c A LaTex expression showing nsquare root of 3 + {n} to the power of 4 square root of 2
2
Simplify, then add or subtract the radical expressions
A LaTex expression showing square root of 2{n to the power of 3 } - square root of 18{n to the power of 3 }
a A LaTex expression showing -2nsquare root of 2n
b A LaTex expression showing 2nsquare root of {n to the power of 2 } - {n} to the power of 3 square root of 3{n to the power of 3 }
c A LaTex expression showing -2nsquare root of 2{n to the power of 2 }
d A LaTex expression showing nsquare root of 5{n to the power of 2 } - 6{n} to the power of 2 square root of {n to the power of 3 }
e A LaTex expression showing -2nsquare root of 2{n to the power of -1 }
f A LaTex expression showing -2{n} to the power of 2 square root of 2n
3
Simplify, then add or subtract the radical expressions
A LaTex expression showing square root of 27{d to the power of 2 } - square root of 3{d to the power of 2 }
a A LaTex expression showing 2d
b A LaTex expression showing 2dsquare root of 5 - 2{d} to the power of 3 square root of 4
c A LaTex expression showing 2{d} to the power of 2 square root of 3
d A LaTex expression showing 2dsquare root of 3
e A LaTex expression showing 4dsquare root of 3
f A LaTex expression showing 2square root of 3
4
Simplify, then add or subtract the radical expressions
A LaTex expression showing square root of 125{p to the power of 4 } - square root of 5{p to the power of 2 }
a A LaTex expression showing {p} to the power of 2 square root of 7 - 3{p} to the power of 2 square root of 4
b A LaTex expression showing 2{p} to the power of 3 square root of 8 - psquare root of 4
c A LaTex expression showing 4psquare root of 7 - 4psquare root of 5
d A LaTex expression showing 5p - psquare root of 2
e A LaTex expression showing 5{p} to the power of 2 square root of 5 - psquare root of 5
f A LaTex expression showing 3p - 2psquare root of 4
5
Simplify, then add or subtract the radical expressions
A LaTex expression showing square root of 275{r to the power of 3 } - square root of 11r
a A LaTex expression showing 2rsquare root of 11{r to the power of 2 } - square root of 7r
b A LaTex expression showing 8rsquare root of 7{r to the power of 2 } - 4square root of 11{r to the power of 3 }
c A LaTex expression showing 5rsquare root of 9r - square root of 10{r to the power of 3 }
d A LaTex expression showing 5rsquare root of 11r - square root of 11r
e A LaTex expression showing 5rsquare root of 13r - square root of 14r
f A LaTex expression showing 5{r} to the power of 2 square root of 9r - square root of 12r
6
Simplify, then add or subtract the radical expressions
A LaTex expression showing square root of 176{b to the power of 4 } + square root of 11{b to the power of 3 }
a A LaTex expression showing 4{b} to the power of 3 square root of 13 + bsquare root of 8b
b A LaTex expression showing {b} to the power of 2 square root of 7 + 4{b} to the power of 2 square root of 12b
c A LaTex expression showing 2bsquare root of 10 + bsquare root of 7b
d A LaTex expression showing 4{b} to the power of 2 square root of 11 + bsquare root of 11b
e A LaTex expression showing {b} to the power of 4 square root of 11 + 2bsquare root of 9{b to the power of 2 }
7
Simplify, then add or subtract the radical expressions
A LaTex expression showing square root of 3{r to the power of 4 } - square root of 27{r to the power of 3 }
a A LaTex expression showing {r} to the power of 2 - rsquare root of r
b A LaTex expression showing {r} to the power of 2 square root of 3 - 3rsquare root of 3r
c A LaTex expression showing {r} to the power of 3 square root of 6 - 4{r} to the power of 3 square root of 5r
d A LaTex expression showing rsquare root of 2 - 2rsquare root of 4{r to the power of 2 }
e A LaTex expression showing 3{r} to the power of 3 - 4rsquare root of 6{r to the power of 3 }
f A LaTex expression showing 3{r} to the power of 4 - rsquare root of 6r