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Radicals - Adding and Subtracting - Simplification (Values and Variables) (Level 5)

This math topic focuses on skills related to radicals involving simplification of expressions with variables and constants to prepare them for addition and subtraction. These problems include various complexities such as square roots and cube roots combined with algebraic expressions involving powers and coefficients. The expressions require both understanding of radical rules and algebraic manipulation to simplify before performing operations like addition or subtraction.

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

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Adding and Subtracting - Simplification (Values and Variables)

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

Simplify the radical expressions to prepare for adding or subtracting

28d2z4+28d3−112\sqrt{28{d}^{2}{z}^{4}} + \sqrt{28{d}^{3}} - \sqrt{112}

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 5)'. 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 27 + square root of 48{r to the power of 2 {c} to the power of 4 } - square root of 27r{c to the power of 4 }
a A LaTex expression showing 3square root of 3 + r{c} to the power of 4 - 3{c} to the power of 2 square root of 3r
b A LaTex expression showing 3square root of 3 + 4r{c} to the power of 2 square root of 3 - 3{c} to the power of 4 square root of 2r
c A LaTex expression showing 3square root of 3 + {r} to the power of 2 {c} to the power of 3 square root of 5 - 3{c} to the power of 2 square root of 3r
d A LaTex expression showing 3square root of 3 + 4r{c} to the power of 2 square root of 3 - 3{c} to the power of 2 square root of 3r
e A LaTex expression showing 3square root of 4 + 4r{c} to the power of 2 square root of 3 - 3{c} to the power of 3 square root of 6r
f A LaTex expression showing 4 + 4r{c} to the power of 2 square root of 3 - 3{c} to the power of 2 square root of 3r
2
Simplify the radical expressions to prepare for adding or subtracting
A LaTex expression showing 3-th root of 88{z to the power of 2 x} + 3-th root of 704x + 3-th root of 88{x to the power of 2 }
a A LaTex expression showing 3-th root of 9{z to the power of 2 x} + 43-th root of 11x + 23-th root of 11{x to the power of 2 }
b A LaTex expression showing 33-th root of 13{z to the power of 2 x} + 43-th root of 11x + 23-th root of 11{x to the power of 2 }
c A LaTex expression showing 53-th root of 13z{x to the power of 2 } + 43-th root of 11x + 23-th root of 11{x to the power of 2 }
d A LaTex expression showing 23-th root of 11{z to the power of 2 x} + 3-th root of 9x + 23-th root of 11{x to the power of 2 }
e A LaTex expression showing 3-th root of 14{z to the power of 3 {x} to the power of 3 } + 3-th root of 9{x to the power of 2 } + 23-th root of 11{x to the power of 2 }
f A LaTex expression showing 23-th root of 11{z to the power of 2 x} + 43-th root of 11x + 23-th root of 11{x to the power of 2 }
3
Simplify the radical expressions to prepare for adding or subtracting
A LaTex expression showing square root of 12{y to the power of 3 {z} to the power of 2 } - square root of 27{y to the power of 3 } - square root of 27{z to the power of 4 }
a A LaTex expression showing yzsquare root of {y to the power of 2 } - 3ysquare root of 3y - 3{z} to the power of 2 square root of 3
b A LaTex expression showing 2yzsquare root of 3y - 2{y} to the power of 2 square root of 3{y to the power of 3 } - 3{z} to the power of 2 square root of 3
c A LaTex expression showing 2yzsquare root of 3y - 6ysquare root of {y to the power of 3 } - 2{z} to the power of 4
d A LaTex expression showing 2yzsquare root of 3y - 6ysquare root of 4y - 3{z} to the power of 2 square root of 3
e A LaTex expression showing 2yzsquare root of 3y - 3ysquare root of 3y - 3{z} to the power of 2 square root of 3
f A LaTex expression showing 4{y} to the power of 3 zsquare root of 4y - 3ysquare root of 3y - 3{z} to the power of 2 square root of 3
4
A LaTex expression showing 3-th root of 448p + 3-th root of 448{m to the power of 3 {p} to the power of 4 } + 3-th root of 56{m to the power of 3 {p} to the power of 4 }
Simplify the radical expressions to prepare for adding or subtracting
a A LaTex expression showing 33-th root of 9p + 3m{p} to the power of 3 3-th root of 4{p to the power of 3 } + 2mp3-th root of 7p
b A LaTex expression showing 3-th root of 9{p to the power of 2 } + 4mp3-th root of 7p + 2mp3-th root of 7p
c A LaTex expression showing 43-th root of 6{p to the power of 3 } + 4mp3-th root of 7{p to the power of 2 } + 2mp3-th root of 7p
d A LaTex expression showing 43-th root of 7p + 4mp3-th root of 7p + 2mp3-th root of 7p
e A LaTex expression showing 43-th root of 7p + 4mp3-th root of 7p + m{p} to the power of 3 3-th root of 7p
f A LaTex expression showing 3-th root of 9p + 4mp3-th root of 7p + 2mp3-th root of 7p
5
Simplify the radical expressions to prepare for adding or subtracting
A LaTex expression showing square root of 125{y to the power of 4 } + square root of 125p - square root of 80{y to the power of 3 {p} to the power of 2 }
a A LaTex expression showing 3ysquare root of 6 + 5square root of 5p - 4ypsquare root of 5y
b A LaTex expression showing 5{y} to the power of 2 square root of 5 + 8square root of 6p - 7y{p} to the power of 3 square root of {y to the power of 2 }
c A LaTex expression showing 4ysquare root of 4 + 5square root of 5p - 4ypsquare root of 5y
d A LaTex expression showing 5{y} to the power of 2 square root of 5 + 5square root of 8p - {y} to the power of 3 psquare root of {y to the power of 2 }
e A LaTex expression showing 5{y} to the power of 2 square root of 5 + 5square root of 5p - 4ypsquare root of 5y
f A LaTex expression showing 5y + 7square root of 4p - 7y{p} to the power of 3 square root of 7y
6
Simplify the radical expressions to prepare for adding or subtracting
A LaTex expression showing square root of 45{x to the power of 3 {n} to the power of 2 } + square root of 45{x to the power of 2 } + square root of 20{x to the power of 4 n}
a A LaTex expression showing 2{x} to the power of 3 nsquare root of 2{x to the power of 2 } + {x} to the power of 3 square root of 4 + xsquare root of 7{n to the power of 2 }
b A LaTex expression showing 3xnsquare root of 5x + {x} to the power of 2 square root of 5 + 2{x} to the power of 2 square root of 5n
c A LaTex expression showing 3xnsquare root of 5x + 3xsquare root of 5 + 2{x} to the power of 2 square root of 5n
d A LaTex expression showing 2xnsquare root of 2x + 3xsquare root of 5 + {x} to the power of 3 square root of 2n
e A LaTex expression showing 3xnsquare root of 5x + 2xsquare root of 4 + 2{x} to the power of 2 square root of 5n
f A LaTex expression showing 3xnsquare root of 5x + 3{x} to the power of 3 square root of 2 + 5xsquare root of 2n
7
Simplify the radical expressions to prepare for adding or subtracting
A LaTex expression showing square root of 44{r to the power of 3 } + square root of 275{r to the power of 3 } - square root of 275{r to the power of 2 }
a A LaTex expression showing 5rsquare root of 9r + 5rsquare root of 11r - 5rsquare root of 11
b A LaTex expression showing 2rsquare root of 11r + 5rsquare root of 11r - 8{r} to the power of 2 square root of 8
c A LaTex expression showing rsquare root of 10r + 5rsquare root of 11r - 5rsquare root of 11
d A LaTex expression showing 2rsquare root of 11r + 5rsquare root of 11r - 5rsquare root of 11
e A LaTex expression showing 4rsquare root of 12r + 5rsquare root of 11r - 5rsquare root of 11
f A LaTex expression showing 2rsquare root of 11r + rsquare root of 12{r to the power of 3 } - 5rsquare root of 11