HomePricing
Sign InJoin

Radicals - 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.

View Unit

Adding and Subtracting from Simplified (Values and Variables)

Complete these online problems with 80% or 4 correct answers in a row. Results are immediate.

Add or subtract the radical expressions

23p+4p232\sqrt{3p} + 4{p}^{2}\sqrt{3}

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

Mobius Math Club logo
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 2{z} to the power of 2 square root of 7 + 3{z} to the power of 2 square root of 7
a A LaTex expression showing {z} to the power of 2 square root of 7
b A LaTex expression showing 5{z} to the power of 2 square root of 7 + 4zsquare root of 7
c A LaTex expression showing 5{z} to the power of 2 square root of 7
d A LaTex expression showing 4zsquare root of 9 + 5{z} to the power of 4 square root of 3
e A LaTex expression showing 5{z} to the power of 4 square root of 7
f A LaTex expression showing 5{z} to the power of 3 square root of 7
2
Add or subtract the radical expressions
A LaTex expression showing 5zsquare root of 2 + 3{z} to the power of 2 square root of 2
a A LaTex expression showing 5zsquare root of 5 + z
b A LaTex expression showing zsquare root of 4 + 4z
c A LaTex expression showing 3{z} to the power of 2 + 3zsquare root of 2
d A LaTex expression showing 4{z} to the power of 3
e A LaTex expression showing 7zsquare root of 3 + 2z
f A LaTex expression showing 5zsquare root of 2 + 3{z} to the power of 2 square root of 2
3
Add or subtract the radical expressions
A LaTex expression showing 4square root of 2b - 5bsquare root of 2
a A LaTex expression showing 2square root of b - 3b
b A LaTex expression showing 4square root of 2b - 5bsquare root of 2
c A LaTex expression showing 2square root of {b to the power of 2 } - 5bsquare root of 2
d A LaTex expression showing square root of 2b - 3{b} to the power of 3
e A LaTex expression showing 3square root of b - 6{b} to the power of 2 square root of 3
f A LaTex expression showing 2square root of b - 3bsquare root of 2
4
Add or subtract the radical expressions
A LaTex expression showing 2msquare root of 3m - 5square root of 3
a A LaTex expression showing 4msquare root of {m to the power of 3 } - 3
b A LaTex expression showing msquare root of m - 8square root of 4
c A LaTex expression showing 3{m} to the power of 3 square root of m - 5square root of 6
d A LaTex expression showing 2msquare root of 3m - 5square root of 3
e A LaTex expression showing 3msquare root of 2m - 2
f A LaTex expression showing {m} to the power of 2 square root of 5m - 8square root of 2
5
Add or subtract the radical expressions
A LaTex expression showing 3square root of 2r - 4square root of 2
a A LaTex expression showing 5square root of {r to the power of 3 } - 2square root of 4
b A LaTex expression showing 3square root of 3r - 2
c A LaTex expression showing 4square root of 3r - 3
d A LaTex expression showing 5square root of 3{r to the power of 2 } - 7
e A LaTex expression showing 6square root of r - 3
f A LaTex expression showing 3square root of 2r - 4square root of 2
6
Add or subtract the radical expressions
A LaTex expression showing 2rsquare root of 7 + 5rsquare root of 7r
a A LaTex expression showing 2rsquare root of 7 + 5rsquare root of 7r
b A LaTex expression showing 4rsquare root of 4 + 7rsquare root of 7r
c A LaTex expression showing 3rsquare root of 10 + 2{r} to the power of 2 square root of 4{r to the power of 3 }
d A LaTex expression showing {r} to the power of 3 square root of 7 + {r} to the power of 3 square root of 9r
e A LaTex expression showing 5{r} to the power of 3 square root of 9 + 6rsquare root of 7r
7
Add or subtract the radical expressions
A LaTex expression showing 3rsquare root of 3 + 4square root of 3r
a A LaTex expression showing rsquare root of 5 + 6square root of 2r
b A LaTex expression showing 2{r} to the power of 3 square root of 3 + 5square root of 6r
c A LaTex expression showing 3rsquare root of 3 + 4square root of 3r
d A LaTex expression showing rsquare root of 6 + 6square root of r
e A LaTex expression showing 5r + 5square root of 4r