Adding and Subtracting - Simplification (Values Only) (Level 4)

These problems focus on simplifying radical expressions as preparation for adding and subtracting them. The exercises involve handling various roots such as square roots and cube roots of different numbers. Each question is structured with an expression needing simplification and provides multiple choices as possible answers. This topic builds foundational skills necessary for more complex algebraic manipulations involving radicals.

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

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Radicals - Adding and Subtracting - Simplification (Values Only) Worksheet

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Radicals - Adding and Subtracting - Simplification (Values Only)
1
Simplify the radical expressions to prepare for adding or subtracting
A LaTex expression showing square root of 112 + square root of 112 - square root of 63
a A LaTex expression showing 4square root of 7 + 3square root of 7 - 3square root of 7
b A LaTex expression showing 4square root of 7 + 5square root of 10 - 3square root of 7
c A LaTex expression showing 4square root of 7 + 4square root of 7 - 3square root of 7
d A LaTex expression showing 3square root of 5 + 5square root of 6 - 3square root of 7
e A LaTex expression showing square root of 7 + 4square root of 7 - 3square root of 7
2
Simplify the radical expressions to prepare for adding or subtracting
A LaTex expression showing square root of 12 + square root of 48 - square root of 12
a A LaTex expression showing 2square root of 3 + 4square root of 3 - 2square root of 3
b A LaTex expression showing 2 + 3 - 4
c A LaTex expression showing square root of 2 + 4square root of 3 - 2square root of 3
d A LaTex expression showing 4square root of 5 + 2 - 2square root of 3
3
Simplify the radical expressions to prepare for adding or subtracting
A LaTex expression showing square root of 125 - square root of 125 - square root of 45
a A LaTex expression showing 5square root of 5 - 5square root of 5 - 3square root of 5
b A LaTex expression showing 6square root of 6 - 6square root of 2 - 5square root of 8
c A LaTex expression showing 5square root of 5 - 5square root of 5 - square root of 6
d A LaTex expression showing 5square root of 5 - 2square root of 3 - 3square root of 5
e A LaTex expression showing 5square root of 5 - 5square root of 5 - 6square root of 7
4
Simplify the radical expressions to prepare for adding or subtracting
A LaTex expression showing 3-th root of 40 + 3-th root of 40 + 3-th root of 320
a A LaTex expression showing 3-th root of 2 + 23-th root of 5 + 43-th root of 5
b A LaTex expression showing 23-th root of 5 + 23-th root of 5 + 43-th root of 3
c A LaTex expression showing 23-th root of 5 + 23-th root of 5 + 23-th root of 4
d A LaTex expression showing 23-th root of 5 + 23-th root of 5 + 43-th root of 5
e A LaTex expression showing 23-th root of 5 + 43-th root of 4 + 43-th root of 5
5
Simplify the radical expressions to prepare for adding or subtracting
A LaTex expression showing 3-th root of 320 + 3-th root of 40 - 3-th root of 135
a A LaTex expression showing 53-th root of 8 + 23-th root of 5 - 63-th root of 2
b A LaTex expression showing 6 + 23-th root of 5 - 33-th root of 5
c A LaTex expression showing 43-th root of 5 + 3-th root of 2 - 33-th root of 5
d A LaTex expression showing 43-th root of 5 + 23-th root of 5 - 33-th root of 5
6
Simplify the radical expressions to prepare for adding or subtracting
A LaTex expression showing square root of 44 - square root of 275 - square root of 44
a A LaTex expression showing 2square root of 11 - 5square root of 11 - square root of 9
b A LaTex expression showing 2square root of 11 - 6square root of 9 - square root of 14
c A LaTex expression showing 2square root of 11 - 5square root of 11 - 2square root of 11
d A LaTex expression showing 2square root of 11 - 3square root of 8 - square root of 14
7
Simplify the radical expressions to prepare for adding or subtracting
A LaTex expression showing 3-th root of 704 - 3-th root of 297 - 3-th root of 88
a A LaTex expression showing 33-th root of 9 - 33-th root of 11 - 23-th root of 11
b A LaTex expression showing 43-th root of 11 - 33-th root of 11 - 43-th root of 13
c A LaTex expression showing 43-th root of 11 - 33-th root of 11 - 23-th root of 11
d A LaTex expression showing 43-th root of 11 - 3-th root of 14 - 23-th root of 11
e A LaTex expression showing 43-th root of 11 - 3-th root of 10 - 23-th root of 11
8
Simplify the radical expressions to prepare for adding or subtracting
A LaTex expression showing 3-th root of 189 - 3-th root of 448 + 3-th root of 189
a A LaTex expression showing 33-th root of 7 - 43-th root of 7 + 3-th root of 8
b A LaTex expression showing 33-th root of 8 - 43-th root of 7 + 53-th root of 3
c A LaTex expression showing 33-th root of 7 - 43-th root of 7 + 33-th root of 7
d A LaTex expression showing 33-th root of 7 - 43-th root of 7 + 33-th root of 10