Adding and Subtracting - Simplification (Values and Variables) (Level 3)

This math topic focuses on simplifying radical expressions involving various powers and roots, such as square roots combined with integer and variable terms. The challenges specifically involve adding and subtracting these radical expressions after simplification. Each question presents a radical equation with multiple outcomes for students to determine the correct simplified form. The material is designed to enhance understanding of manipulating and combining radicals, tailored for students with prior knowledge, as indicated by the inclusion of values and variables within the 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 and Variables) Worksheet

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Radicals - Adding and Subtracting - Simplification (Values and Variables)
1
Simplify the radical expressions to prepare for adding or subtracting
A LaTex expression showing square root of 27{y to the power of 2 } + square root of 75y
a A LaTex expression showing 5ysquare root of 5 + square root of 3y
b A LaTex expression showing 3ysquare root of 3 + 2square root of 4y
c A LaTex expression showing 3ysquare root of 3 + 5square root of 3y
2
Simplify the radical expressions to prepare for adding or subtracting
A LaTex expression showing square root of 175{n to the power of 3 } - square root of 63{n to the power of 4 }
a A LaTex expression showing 7nsquare root of 6n - 3{n} to the power of 2 square root of 7
b A LaTex expression showing 5nsquare root of 7n - 6{n} to the power of 2 square root of 4
c A LaTex expression showing nsquare root of 9n - 6nsquare root of 10
d A LaTex expression showing 5nsquare root of 7n - 3{n} to the power of 2 square root of 7
e A LaTex expression showing 3nsquare root of 4n - 3{n} to the power of 2 square root of 7
3
Simplify the radical expressions to prepare for adding or subtracting
A LaTex expression showing square root of 125 - square root of 20m
a A LaTex expression showing 5square root of 5 - 4square root of 8m
b A LaTex expression showing 7square root of 2 - 2square root of 5m
c A LaTex expression showing 5square root of 5 - 2square root of 5m
d A LaTex expression showing 5square root of 5 - 4square root of 4{m to the power of 2 }
e A LaTex expression showing 3square root of 6 - 4square root of 7m
4
Simplify the radical expressions to prepare for adding or subtracting
A LaTex expression showing square root of 275x - square root of 176{x to the power of 4 }
a A LaTex expression showing 5square root of 11x - {x} to the power of 2 square root of 10
b A LaTex expression showing 6square root of 8x - 2{x} to the power of 2 square root of 14
c A LaTex expression showing 5square root of 11x - 3{x} to the power of 2 square root of 7
d A LaTex expression showing 5square root of 11x - 4{x} to the power of 2 square root of 11
5
Simplify the radical expressions to prepare for adding or subtracting
A LaTex expression showing square root of 48{z to the power of 4 } + square root of 75z
a A LaTex expression showing 3z + 5square root of 3z
b A LaTex expression showing 7{z} to the power of 4 + 5square root of 3z
c A LaTex expression showing 2{z} to the power of 4 square root of 3 + 5square root of 3z
d A LaTex expression showing 4{z} to the power of 2 square root of 3 + 5square root of 3z
6
Simplify the radical expressions to prepare for adding or subtracting
A LaTex expression showing square root of 125{z to the power of 2 } - square root of 80{z to the power of 4 }
a A LaTex expression showing 5zsquare root of 5 - {z} to the power of 3 square root of 3
b A LaTex expression showing 5{z} to the power of 3 - 4{z} to the power of 2 square root of 5
c A LaTex expression showing 3{z} to the power of 3 square root of 7 - 4{z} to the power of 2 square root of 5
d A LaTex expression showing 7zsquare root of 3 - 4{z} to the power of 2 square root of 5
e A LaTex expression showing 5zsquare root of 5 - 4{z} to the power of 2 square root of 5
7
Simplify the radical expressions to prepare for adding or subtracting
A LaTex expression showing square root of 18y - square root of 8{y to the power of 3 }
a A LaTex expression showing 3square root of 2y - ysquare root of 3{y to the power of 3 }
b A LaTex expression showing 3square root of 2y - 2ysquare root of 2y
c A LaTex expression showing 3square root of 2y - 4{y} to the power of 3 square root of {y to the power of 3 }
8
Simplify the radical expressions to prepare for adding or subtracting
A LaTex expression showing square root of 45 - square root of 125{z to the power of 2 }
a A LaTex expression showing 3square root of 5 - 5zsquare root of 5
b A LaTex expression showing 3square root of 5 - 6zsquare root of 6
c A LaTex expression showing 2square root of 4 - 5{z} to the power of 3