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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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 75{b to the power of 3 } - square root of 48{b to the power of 3 }
a A LaTex expression showing bsquare root of 3{b to the power of 3 }
b A LaTex expression showing bsquare root of 3b
c A LaTex expression showing bsquare root of 3
d A LaTex expression showing bsquare root of 3{b to the power of 2 }
e A LaTex expression showing {b} to the power of 3 square root of 5{b to the power of 2 } - {b} to the power of 2 square root of {b to the power of 3 }
2
A LaTex expression showing square root of 63{p to the power of 2 } + square root of 175p
Simplify, then add or subtract the radical expressions
a A LaTex expression showing {p} to the power of 3 square root of 5 + 7square root of 10p
b A LaTex expression showing 3psquare root of 7 + 5square root of 7p
3
Simplify, then add or subtract the radical expressions
A LaTex expression showing square root of 275y - square root of 99y
a A LaTex expression showing 2square root of 11{y to the power of 3 }
b A LaTex expression showing 5square root of 10y - 6square root of 7y
c A LaTex expression showing 2square root of 11y
d A LaTex expression showing 2square root of y
e A LaTex expression showing 3square root of 14{y to the power of 3 } - 6square root of 8{y to the power of 3 }
4
Simplify, then add or subtract the radical expressions
A LaTex expression showing square root of 80x + square root of 20{x to the power of 4 }
a A LaTex expression showing 4square root of 5x + 2{x} to the power of 2 square root of 5
b A LaTex expression showing square root of 4{x to the power of 2 } + xsquare root of 2
c A LaTex expression showing 3square root of 3{x to the power of 3 } + xsquare root of 2
5
A LaTex expression showing square root of 176x - square root of 99{x to the power of 3 }
Simplify, then add or subtract the radical expressions
a A LaTex expression showing square root of 14{x to the power of 2 } - 2xsquare root of 8x
b A LaTex expression showing 4square root of 11x - 3xsquare root of 11x
6
Simplify, then add or subtract the radical expressions
A LaTex expression showing square root of 275{r to the power of 4 } + square root of 99{r to the power of 2 }
a A LaTex expression showing 4{r} to the power of 3 square root of 13 + 3rsquare root of 13
b A LaTex expression showing 5{r} to the power of 2 square root of 11 + 3rsquare root of 11
c A LaTex expression showing 4{r} to the power of 2 square root of 13 + rsquare root of 7
7
Simplify, then add or subtract the radical expressions
A LaTex expression showing square root of 32{c to the power of 4 } + square root of 50c
a A LaTex expression showing 7c + 4square root of 5{c to the power of 2 }
b A LaTex expression showing 5{c} to the power of 3 + 6square root of c
c A LaTex expression showing 4{c} to the power of 2 square root of 2 + 5square root of 2c
d A LaTex expression showing 3{c} to the power of 4 square root of 5 + 3square root of c