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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Math worksheet on 'Radicals - Adding and Subtracting - Simplification (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
Simplify the radical expressions to prepare for adding or subtracting
A LaTex expression showing square root of 175{b to the power of 3 } - square root of 112{b to the power of 3 }
a A LaTex expression showing 5bsquare root of 7b - 3bsquare root of 8b
b A LaTex expression showing 5bsquare root of 7b - 4bsquare root of 7b
c A LaTex expression showing 5{b} to the power of 3 square root of 3{b to the power of 2 } - bsquare root of 8b
2
Simplify the radical expressions to prepare for adding or subtracting
A LaTex expression showing square root of 32{z to the power of 3 } - square root of 50z
a A LaTex expression showing 7zsquare root of 4z - 5square root of 2z
b A LaTex expression showing 4zsquare root of 2z - 5square root of 2z
c A LaTex expression showing 4zsquare root of 2z - 7square root of {z to the power of 2 }
3
Simplify the radical expressions to prepare for adding or subtracting
A LaTex expression showing square root of 28 + square root of 112{x to the power of 3 }
a A LaTex expression showing square root of 3 + 7xsquare root of 4x
b A LaTex expression showing 2square root of 7 + 6{x} to the power of 2 square root of 5x
c A LaTex expression showing 3square root of 8 + 2xsquare root of 6x
d A LaTex expression showing 2square root of 7 + 4xsquare root of 7x
4
Simplify the radical expressions to prepare for adding or subtracting
A LaTex expression showing square root of 32{z to the power of 2 } - square root of 18z
a A LaTex expression showing 4zsquare root of 2 - 3square root of z
b A LaTex expression showing 4zsquare root of 2 - 3square root of 2z
c A LaTex expression showing {z} to the power of 3 - 3square root of 5{z to the power of 3 }
d A LaTex expression showing 7z - 3square root of 2z
5
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 3{z} to the power of 3 square root of 7 - 4{z} to the power of 2 square root of 5
b A LaTex expression showing 5zsquare root of 5 - 4{z} to the power of 2 square root of 5
c A LaTex expression showing 5{z} to the power of 3 - 4{z} to the power of 2 square root of 5
d A LaTex expression showing 5zsquare root of 5 - {z} to the power of 3 square root of 3
e A LaTex expression showing 7zsquare root of 3 - 4{z} to the power of 2 square root of 5
6
Simplify the radical expressions to prepare for adding or subtracting
A LaTex expression showing square root of 44z - square root of 176{z to the power of 3 }
a A LaTex expression showing 2square root of 10z - 4zsquare root of 11z
b A LaTex expression showing 2square root of 11z - 4zsquare root of 11z
c A LaTex expression showing 2square root of 11z - 3{z} to the power of 3 square root of 14z
7
Simplify the radical expressions to prepare for adding or subtracting
A LaTex expression showing square root of 44{x to the power of 3 } + square root of 99{x to the power of 2 }
a A LaTex expression showing 2xsquare root of 11x + 2xsquare root of 8
b A LaTex expression showing {x} to the power of 2 square root of 10x + 3xsquare root of 11
c A LaTex expression showing 2xsquare root of 11x + {x} to the power of 2 square root of 9
d A LaTex expression showing 2xsquare root of 11x + 3xsquare root of 11