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

This math topic focuses on the practice of adding and subtracting radicals, specifically covering both radicals involving numerical values and those with variables. Each of the seven questions requires the student to simplify radical expressions, then perform addition or subtraction. The radical expressions vary across different indices and include mixed variables, testing a student's ability to manipulate and simplify under root terms systematically. This is part of introductory learning to radical addition and subtraction.

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

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Radicals - Adding and Subtracting (Values and Variables) Worksheet

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Radicals - Adding and Subtracting (Values and Variables)
1
A LaTex expression showing square root of 112{x to the power of 3 m} + square root of 28{x to the power of 4 {m} to the power of 3 } - square root of 112{x to the power of 4 {m} to the power of 3 }
Simplify, then add or subtract the radical expressions
a A LaTex expression showing 4xsquare root of 7xm - 2{x} to the power of 2 msquare root of 7{m to the power of 3 }
b A LaTex expression showing 4{x} to the power of 2 square root of 4{x to the power of 3 {m} to the power of 3 } + {x} to the power of 4 {m} to the power of 3 square root of 10m - 7xmsquare root of 6m
c A LaTex expression showing 4xsquare root of 7xm + {x} to the power of 2 msquare root of 7m
d A LaTex expression showing 4xsquare root of 7xm - 2{x} to the power of 2 msquare root of 7
e A LaTex expression showing 4xsquare root of 7xm - 2{x} to the power of 2 msquare root of 7m
2
A LaTex expression showing square root of 63{y to the power of 2 {m} to the power of 3 } + square root of 175{y to the power of 2 m} - square root of 112{m to the power of 4 }
Simplify, then add or subtract the radical expressions
a A LaTex expression showing 4ymsquare root of 4m + 6ysquare root of 4{m to the power of 3 } - 7{m} to the power of 3 square root of 3
b A LaTex expression showing 3ymsquare root of 7m + 5ysquare root of 7m - 4{m} to the power of 2 square root of 7
c A LaTex expression showing 5ymsquare root of 3{m to the power of 2 } + 7ysquare root of 6{m to the power of 2 } - 3msquare root of 6
d A LaTex expression showing 6y{m} to the power of 2 square root of 3m + 8ysquare root of 8m - 3msquare root of 8
3
Simplify, then add or subtract the radical expressions
A LaTex expression showing 3-th root of 192{c to the power of 2 } + 3-th root of 24{c to the power of 2 {d} to the power of 4 } - 3-th root of 192{c to the power of 4 }
a A LaTex expression showing 3-th root of 4{c to the power of 3 } + d3-th root of 2{c to the power of 4 {d} to the power of 3 } - 4c3-th root of c
b A LaTex expression showing 43-th root of 3{c to the power of 2 } + 2d3-th root of 3{c to the power of 2 d} - 4c3-th root of 3c
c A LaTex expression showing 53-th root of 3{c to the power of 2 } + 2d3-th root of 4{c to the power of 2 {d} to the power of 2 } - {c} to the power of 2 3-th root of 3c
4
Simplify, then add or subtract the radical expressions
A LaTex expression showing 3-th root of 297{c to the power of 3 {d} to the power of 2 } + 3-th root of 297cd - 3-th root of 88{c to the power of 3 {d} to the power of 2 }
a A LaTex expression showing {c} to the power of 3 3-th root of 11{d to the power of 3 } + 23-th root of 9cd - 3c3-th root of 10d
b A LaTex expression showing c3-th root of 11{d to the power of 2 } + 33-th root of 11cd
c A LaTex expression showing 3-th root of 11{d to the power of 2 } + 33-th root of 11cd
d A LaTex expression showing c3-th root of {d to the power of 2 } + 33-th root of 11cd
e A LaTex expression showing 4c3-th root of 11{d to the power of 2 } + 33-th root of 11cd
5
Simplify, then add or subtract the radical expressions
A LaTex expression showing 3-th root of 128{y to the power of 4 } + 3-th root of 128{x to the power of 4 } + 3-th root of 54{x to the power of 2 y}
a A LaTex expression showing 4{y} to the power of 3 3-th root of 3y + 3x3-th root of x + 3-th root of 5x{y to the power of 3 }
b A LaTex expression showing 7{y} to the power of 3 3-th root of y + 3{x} to the power of 3 3-th root of 2{x to the power of 3 } + 3-th root of 4{x to the power of 2 y}
c A LaTex expression showing 4y3-th root of 2y + 4x3-th root of 2x + 33-th root of 2{x to the power of 2 y}
6
Simplify, then add or subtract the radical expressions
A LaTex expression showing square root of 75{z to the power of 3 p} - square root of 48{z to the power of 3 } + square root of 27{z to the power of 3 {p} to the power of 2 }
a A LaTex expression showing 5zsquare root of 3zp - 4zsquare root of 3z + 3zpsquare root of 3z
b A LaTex expression showing 4zsquare root of z{p to the power of 3 } - 7zsquare root of z + 3zpsquare root of 4{z to the power of 3 }
c A LaTex expression showing 2zsquare root of 6zp - 5{z} to the power of 3 square root of {z to the power of 2 } + 2{z} to the power of 3 {p} to the power of 2 square root of z
d A LaTex expression showing 5zsquare root of zp - 7zsquare root of {z to the power of 2 } + zpsquare root of 5z
7
A LaTex expression showing 3-th root of 40{p to the power of 4 m} - 3-th root of 320{p to the power of 4 } - 3-th root of 320{p to the power of 2 {m} to the power of 4 }
Simplify, then add or subtract the radical expressions
a A LaTex expression showing 3p3-th root of 7{p to the power of 3 m} - 4p3-th root of 8{p to the power of 2 } - 7m3-th root of 7{p to the power of 3 m}
b A LaTex expression showing 4p3-th root of 6{p to the power of 2 {m} to the power of 2 } - 5p3-th root of 7p - 6{m} to the power of 2 3-th root of 3{p to the power of 4 m}
c A LaTex expression showing 2p3-th root of 5pm - 4p3-th root of 5p - 4m3-th root of 5{p to the power of 2 m}
d A LaTex expression showing {p} to the power of 3 3-th root of 4pm - p3-th root of 2{p to the power of 2 } - 4m3-th root of 2{p to the power of 4 m}
8
Simplify, then add or subtract the radical expressions
A LaTex expression showing 3-th root of 16{d to the power of 4 z} + 3-th root of 54{d to the power of 4 {z} to the power of 4 } + 3-th root of 16{z to the power of 3 }
a A LaTex expression showing 2d3-th root of 2dz + 3dz3-th root of 2dz + 2z3-th root of 2
b A LaTex expression showing d3-th root of {d to the power of 2 z} + 4dz3-th root of dz + {z} to the power of 2
c A LaTex expression showing {d} to the power of 2 3-th root of 3dz + 5dz3-th root of 4{d to the power of 2 {z} to the power of 2 } + 5z3-th root of 4