Adding and Subtracting from Simplified (Values and Variables) (Level 3)

This math topic focuses on adding and subtracting radical expressions involving both numerical values and variables. The problems are designed to help students practice simplifying and combining radicals that contain algebraic expressions. Some problems include expressions with different roots and powers, requiring knowledge of radical rules to add or subtract effectively. This involves manipulating expressions for addition or subtraction by ensuring the radicals have the same index and radicand, and appropriately handling coefficients and variables within the radical expressions.

Work on practice problems directly here, or download the printable pdf worksheet to practice offline.

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Radicals - Adding and Subtracting from Simplified (Values and Variables) Worksheet

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Math worksheet on 'Radicals - Adding and Subtracting from Simplified (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
Add or subtract the radical expressions
A LaTex expression showing 2square root of 11r + 3{r} to the power of 2 square root of 11
a A LaTex expression showing square root of 13r + {r} to the power of 4 square root of 11
b A LaTex expression showing 5square root of 8{r to the power of 3 } + 3{r} to the power of 4 square root of 9
c A LaTex expression showing square root of 9r + {r} to the power of 2 square root of 14
d A LaTex expression showing 2square root of 11r + 3{r} to the power of 2 square root of 11
2
Add or subtract the radical expressions
A LaTex expression showing 2{d} to the power of 2 square root of 3 - 3dsquare root of 3
a A LaTex expression showing {d} to the power of 3 square root of 4 - 2d
b A LaTex expression showing 2{d} to the power of 2 square root of 3 - 3dsquare root of 3
c A LaTex expression showing 3d - dsquare root of 3
3
Add or subtract the radical expressions
A LaTex expression showing 4rsquare root of 3r + 2square root of 3r
a A LaTex expression showing 4rsquare root of 3r + 2square root of 3r
b A LaTex expression showing 4rsquare root of {r to the power of 2 } + square root of r
c A LaTex expression showing 2rsquare root of r + square root of 3r
4
Add or subtract the radical expressions
A LaTex expression showing 4square root of 7p + 3square root of 7p
a A LaTex expression showing 7square root of 7{p to the power of 3 }
b A LaTex expression showing 7square root of p
c A LaTex expression showing 4square root of 4p + 4square root of 8p
d A LaTex expression showing 5square root of 7p
e A LaTex expression showing 7square root of 7p
5
Add or subtract the radical expressions
A LaTex expression showing 4nsquare root of 2n - 5{n} to the power of 2 square root of 2
a A LaTex expression showing 4nsquare root of 2n - 5{n} to the power of 2 square root of 2
b A LaTex expression showing 5{n} to the power of 2 square root of n - 6{n} to the power of 3
c A LaTex expression showing 7{n} to the power of 3 square root of 2n - 3n
d A LaTex expression showing 5{n} to the power of 3 square root of {n to the power of 2 } - 6{n} to the power of 4 square root of 4
6
Add or subtract the radical expressions
A LaTex expression showing 2nsquare root of 5 - 3{n} to the power of 2 square root of 5
a A LaTex expression showing 2n - 6{n} to the power of 4 square root of 8
b A LaTex expression showing 2nsquare root of 6 - 6nsquare root of 3
c A LaTex expression showing 2nsquare root of 5 - 3{n} to the power of 2 square root of 5
7
Add or subtract the radical expressions
A LaTex expression showing 4{x} to the power of 2 square root of 3 - 3square root of 3x
a A LaTex expression showing 2x - square root of 4x
b A LaTex expression showing 4{x} to the power of 2 square root of 3 - 3square root of 3x
c A LaTex expression showing 3xsquare root of 4 - 3square root of x
d A LaTex expression showing {x} to the power of 3 - square root of 3{x to the power of 2 }