Adding and Subtracting - Simplification (Values Only) (Level 5)

This math topic focuses on simplifying radical expressions for subsequent addition and subtraction. It involves various levels and questions that require students to simplify expressions involving square roots, cube roots, and other nth roots before combining them, ensuring that the expressions are in their simplest form to facilitate accurate calculation. This skill is fundamental to higher-level algebra and helps in solving complex equations efficiently by reducing the complexity of 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 3-th root of 16 - 3-th root of 54 + 3-th root of 16
a A LaTex expression showing 23-th root of 2 - 33-th root of 2 + 3-th root of 5
b A LaTex expression showing 23-th root of 2 - 1 + 23-th root of 2
c A LaTex expression showing 23-th root of 2 - 33-th root of 2 + 23-th root of 2
d A LaTex expression showing 3-th root of 5 - 43-th root of 3 + 23-th root of 2
2
Simplify the radical expressions to prepare for adding or subtracting
A LaTex expression showing 3-th root of 128 + 3-th root of 54 + 3-th root of 16
a A LaTex expression showing 3-th root of 5 + 3-th root of 3 + 3-th root of 3
b A LaTex expression showing 43-th root of 2 + 33-th root of 2 + 23-th root of 2
c A LaTex expression showing 43-th root of 2 + 1 + 3-th root of 5
d A LaTex expression showing 2 + 33-th root of 2 + 5
3
Simplify the radical expressions to prepare for adding or subtracting
A LaTex expression showing 3-th root of 448 - 3-th root of 448 + 3-th root of 56
a A LaTex expression showing 43-th root of 7 - 43-th root of 7 + 23-th root of 7
b A LaTex expression showing 43-th root of 7 - 43-th root of 7 + 43-th root of 9
c A LaTex expression showing 33-th root of 7 - 43-th root of 7 + 23-th root of 7
d A LaTex expression showing 43-th root of 7 - 73-th root of 8 + 23-th root of 7
4
Simplify the radical expressions to prepare for adding or subtracting
A LaTex expression showing square root of 12 + square root of 75 - square root of 27
a A LaTex expression showing 2square root of 3 + 7square root of 6 - 3square root of 6
b A LaTex expression showing 1 + 5square root of 3 - 4square root of 3
c A LaTex expression showing 2square root of 3 + 5square root of 3 - 3square root of 3
d A LaTex expression showing 1 + 6 - 3square root of 3
5
Simplify the radical expressions to prepare for adding or subtracting
A LaTex expression showing square root of 45 + square root of 20 + square root of 125
a A LaTex expression showing 3square root of 5 + 2square root of 5 + 3
b A LaTex expression showing 3square root of 5 + 2square root of 5 + 5square root of 5
c A LaTex expression showing 3square root of 5 + 2square root of 5 + square root of 5
d A LaTex expression showing 2square root of 4 + 2square root of 5 + 5square root of 5
6
Simplify the radical expressions to prepare for adding or subtracting
A LaTex expression showing square root of 175 - square root of 112 - square root of 175
a A LaTex expression showing 5square root of 7 - 5square root of 10 - 5square root of 8
b A LaTex expression showing 5square root of 7 - 4square root of 10 - 5square root of 7
c A LaTex expression showing 5square root of 6 - 7square root of 7 - 5square root of 7
d A LaTex expression showing 5square root of 7 - 4square root of 7 - 5square root of 7
e A LaTex expression showing 5square root of 6 - 4square root of 7 - 5square root of 7
7
Simplify the radical expressions to prepare for adding or subtracting
A LaTex expression showing 3-th root of 448 - 3-th root of 56 - 3-th root of 189
a A LaTex expression showing 43-th root of 7 - 23-th root of 7 - 33-th root of 7
b A LaTex expression showing 43-th root of 7 - 33-th root of 10 - 33-th root of 7
c A LaTex expression showing 33-th root of 10 - 23-th root of 7 - 33-th root of 7
8
Simplify the radical expressions to prepare for adding or subtracting
A LaTex expression showing 3-th root of 56 + 3-th root of 56 + 3-th root of 448
a A LaTex expression showing 23-th root of 7 + 23-th root of 7 + 43-th root of 7
b A LaTex expression showing 33-th root of 3 + 23-th root of 7 + 43-th root of 7
c A LaTex expression showing 23-th root of 7 + 23-th root of 3 + 43-th root of 7
d A LaTex expression showing 53-th root of 8 + 3-th root of 9 + 43-th root of 7
e A LaTex expression showing 23-th root of 7 + 3-th root of 4 + 43-th root of 7