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

This math topic focuses on the addition and subtraction of radical expressions, specifically emphasizing their simplification involving both numerical values and variables. Students engage in combining like terms and simplifying under the radical, requiring a good understanding of exponent rules, multiplication, and division within the context of radicals. The topic forms a part of an introduction to more advanced algebraic techniques dealing with radical expressions. The questions include both square roots and higher-order roots, and covers scenarios including different powers and coefficients to challenge and improve algebraic manipulation skills related to radicals.

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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 4)'. 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 125{x to the power of 3 {p} to the power of 2 } - square root of 20{p to the power of 3 } + square root of 20x{p to the power of 4 }
a A LaTex expression showing 5xpsquare root of 5x - 2psquare root of 5p + 2{p} to the power of 2 square root of 5x
b A LaTex expression showing {x} to the power of 2 psquare root of 4x - psquare root of {p to the power of 3 } + 2{p} to the power of 2 square root of 5x
c A LaTex expression showing 5xpsquare root of 5x - 2psquare root of 5p + {p} to the power of 2 square root of x
2
Simplify the radical expressions to prepare for adding or subtracting
A LaTex expression showing 3-th root of 448{p to the power of 4 z} + 3-th root of 448{z to the power of 4 } + 3-th root of 56{p to the power of 3 }
a A LaTex expression showing 4p3-th root of 7pz + 4z3-th root of 7z + {p} to the power of 3 3-th root of 3
b A LaTex expression showing 4p3-th root of 7pz + 4z3-th root of 7z + 2{p} to the power of 2 3-th root of 4
c A LaTex expression showing 4p3-th root of 7pz + 4z3-th root of 7z + 2p3-th root of 7
d A LaTex expression showing 2p3-th root of 8pz + 2{z} to the power of 2 3-th root of 4z + {p} to the power of 3 3-th root of 8
3
Simplify the radical expressions to prepare for adding or subtracting
A LaTex expression showing 3-th root of 81 + 3-th root of 24{p to the power of 2 {b} to the power of 2 } - 3-th root of 24{b to the power of 2 }
a A LaTex expression showing 2 + 23-th root of 3{p to the power of 2 {b} to the power of 2 } - 23-th root of 3{b to the power of 2 }
b A LaTex expression showing 33-th root of 3 + 23-th root of 3{p to the power of 2 {b} to the power of 2 } - 23-th root of 3{b to the power of 2 }
c A LaTex expression showing 6 + 23-th root of 3{p to the power of 2 {b} to the power of 2 } - 23-th root of 3{b to the power of 2 }
4
Simplify the radical expressions to prepare for adding or subtracting
A LaTex expression showing 3-th root of 88{r to the power of 4 {n} to the power of 4 } - 3-th root of 88{n to the power of 3 } + 3-th root of 297{r to the power of 3 {n} to the power of 3 }
a A LaTex expression showing 2rn3-th root of 11rn - 2n3-th root of 11 + 3rn3-th root of 11
b A LaTex expression showing rn3-th root of 10r{n to the power of 3 } - 2n3-th root of 11 + rn3-th root of 9
c A LaTex expression showing rn3-th root of 14rn - 2n3-th root of 11 + 3rn3-th root of 11
d A LaTex expression showing {r} to the power of 2 n3-th root of 11{r to the power of 3 {n} to the power of 2 } - 2n3-th root of 11 + 6{r} to the power of 3 n3-th root of 9
5
Simplify the radical expressions to prepare for adding or subtracting
A LaTex expression showing 3-th root of 88{r to the power of 3 {z} to the power of 2 } + 3-th root of 88{r to the power of 3 {z} to the power of 3 } - 3-th root of 704z
a A LaTex expression showing 2r3-th root of 11{z to the power of 2 } + 2rz3-th root of 11 - 43-th root of 11z
b A LaTex expression showing 2r3-th root of 11{z to the power of 2 } + 3rz3-th root of 10 - 43-th root of 11z
c A LaTex expression showing r3-th root of 8{z to the power of 2 } + 2rz3-th root of 11 - 43-th root of 11z
d A LaTex expression showing 2r3-th root of 11{z to the power of 2 } + {r} to the power of 3 z3-th root of 10 - 53-th root of 12z
6
Simplify the radical expressions to prepare for adding or subtracting
A LaTex expression showing 3-th root of 40r + 3-th root of 135r{y to the power of 2 } - 3-th root of 320{r to the power of 4 }
a A LaTex expression showing 23-th root of 5r + 3-th root of 3r{y to the power of 4 } - 4r3-th root of 5r
b A LaTex expression showing 23-th root of 5r + 33-th root of 5r{y to the power of 2 } - 2{r} to the power of 3 3-th root of 5r
c A LaTex expression showing 23-th root of 5r + 33-th root of 5r{y to the power of 2 } - 4r3-th root of 5r
7
Simplify the radical expressions to prepare for adding or subtracting
A LaTex expression showing 3-th root of 88z - 3-th root of 704 + 3-th root of 704{p to the power of 4 {z} to the power of 3 }
a A LaTex expression showing 23-th root of 11z - 3-th root of 12 + 4pz3-th root of 11p
b A LaTex expression showing 33-th root of 10z - 43-th root of 11 + 4pz3-th root of 11p
c A LaTex expression showing 23-th root of 11z - 43-th root of 11 + 4pz3-th root of 11p
d A LaTex expression showing 23-th root of 11z - 43-th root of 11 + pz3-th root of 10{p to the power of 2 }
Radicals - Adding and Subtracting - Simplification (Values and Variables) (Level 4) - Mobius Math Academy