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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

44x3+11\sqrt{44{x}^{3}} + \sqrt{11}

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 12{z to the power of 4 } - square root of 3{z to the power of 2 }
a A LaTex expression showing 2{z} to the power of 2 square root of 3 - zsquare root of 3
b A LaTex expression showing 4zsquare root of 6 - 3{z} to the power of 2 square root of 5
c A LaTex expression showing 2zsquare root of 4 - 4{z} to the power of 2 square root of 4
d A LaTex expression showing {z} to the power of 3 square root of 6 - {z} to the power of 3 square root of 4
e A LaTex expression showing z - {z} to the power of 3
2
Simplify, then add or subtract the radical expressions
A LaTex expression showing square root of 3y + square root of 48y
a A LaTex expression showing 4square root of 3{y to the power of 3 } + 6square root of 4{y to the power of 2 }
b A LaTex expression showing 8square root of y
c A LaTex expression showing 5square root of 3y
d A LaTex expression showing 5square root of 3{y to the power of 3 }
e A LaTex expression showing 5square root of 3{y to the power of -1 }
f A LaTex expression showing 5square root of 3{y to the power of 2 }
3
Simplify, then add or subtract the radical expressions
A LaTex expression showing square root of 48{b to the power of 2 } + square root of 3{b to the power of 4 }
a A LaTex expression showing {b} to the power of 2 square root of 2 + bsquare root of 3
b A LaTex expression showing 4bsquare root of 3 + {b} to the power of 2 square root of 3
c A LaTex expression showing 7{b} to the power of 3 square root of 5 + bsquare root of 3
d A LaTex expression showing bsquare root of 4 + {b} to the power of 4 square root of 2
e A LaTex expression showing 4bsquare root of 3 + 2bsquare root of 2
f A LaTex expression showing b + bsquare root of 3
4
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 3{r} to the power of 3 - 4rsquare root of 6{r to the power of 3 }
b A LaTex expression showing {r} to the power of 2 - rsquare root of r
c A LaTex expression showing 3{r} to the power of 4 - rsquare root of 6r
d A LaTex expression showing rsquare root of 2 - 2rsquare root of 4{r to the power of 2 }
e A LaTex expression showing {r} to the power of 2 square root of 3 - 3rsquare root of 3r
f 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
5
Simplify, then add or subtract the radical expressions
A LaTex expression showing square root of 176 + square root of 11{c to the power of 4 }
a A LaTex expression showing 7square root of 14 + csquare root of 12
b A LaTex expression showing 4square root of 14 + csquare root of 9
c A LaTex expression showing square root of 11 + {c} to the power of 4 square root of 13
d A LaTex expression showing 2square root of 11 + csquare root of 12
e A LaTex expression showing 4square root of 11 + {c} to the power of 2 square root of 11
f A LaTex expression showing 2square root of 9 + 2csquare root of 9
6
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 -2{n} to the power of 2 square root of 2n
b 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 }
c A LaTex expression showing -2nsquare root of 2n
d A LaTex expression showing -2nsquare root of 2{n to the power of -1 }
e A LaTex expression showing -2nsquare root of 2{n to the power of 2 }
f 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 }
7
Simplify, then add or subtract the radical expressions
A LaTex expression showing square root of 275{m to the power of 3 } + square root of 11{m to the power of 4 }
a A LaTex expression showing 6{m} to the power of 3 square root of 10m + msquare root of 11
b A LaTex expression showing 8msquare root of 9m + 3{m} to the power of 2 square root of 12
c A LaTex expression showing 6{m} to the power of 3 square root of 11m + {m} to the power of 3 square root of 9
d A LaTex expression showing 6{m} to the power of 2 square root of 14m + {m} to the power of 3 square root of 12
e A LaTex expression showing 5msquare root of 11m + {m} to the power of 2 square root of 11
f A LaTex expression showing 5{m} to the power of 2 square root of 7{m to the power of 3 } + 4{m} to the power of 2 square root of 12