Square - Simplifying from Factors, Values and Variables, Radical Remaining (Level 2)

This math topic focuses on simplifying square roots involving factors, values, and variables, with a focus on identifying and simplifying expressions using radical notation. Specific skills practiced include multiplying factors within a radical, simplifying expressions to their simplest radical form, and handling variables within square roots. Each problem presents a radical expression and multiple choice answers, requiring students to apply their understanding of radical properties and arithmetic to select the correct simplified form.

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

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Radicals - Square - Simplifying from Factors, Values and Variables, Radical Remaining Worksheet

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Radicals - Square - Simplifying from Factors, Values and Variables, Radical Remaining
1
Simplify the radical
A LaTex expression showing square root of 3 times 5 times 5 times d times d times d times d times d
a A LaTex expression showing 5dsquare root of 2{d to the power of 3 }
b A LaTex expression showing 7dsquare root of {d to the power of 2 }
c A LaTex expression showing 3{d} to the power of 3 square root of d
d A LaTex expression showing 3{d} to the power of 2 square root of 6d
e A LaTex expression showing 5{d} to the power of 2 square root of 3d
2
Simplify the radical
A LaTex expression showing square root of 3 times 5 times 5 times m times m times m times m
a A LaTex expression showing 3{m} to the power of 3 square root of 3
b A LaTex expression showing 7{m} to the power of 3
c A LaTex expression showing 5{m} to the power of 2 square root of 3
d A LaTex expression showing 5msquare root of 2
e A LaTex expression showing 7msquare root of 4
3
Simplify the radical
A LaTex expression showing square root of 3 times 3 times 11 times n times n times n times n
a A LaTex expression showing 3{n} to the power of 2 square root of 11
b A LaTex expression showing nsquare root of 8
c A LaTex expression showing {n} to the power of 3 square root of 10
d A LaTex expression showing 2{n} to the power of 2 square root of 11
e A LaTex expression showing 6{n} to the power of 4 square root of 14
4
Simplify the radical
A LaTex expression showing square root of 2 times 2 times 2 times 2 times 2 times c times c times c times c times c
a A LaTex expression showing 6{c} to the power of 2 square root of c
b A LaTex expression showing csquare root of 4c
c A LaTex expression showing 6{c} to the power of 3 square root of c
d A LaTex expression showing 4{c} to the power of 2 square root of 2c
e A LaTex expression showing csquare root of 5c
5
Simplify the radical
A LaTex expression showing square root of 2 times 2 times 3 times c times c
a A LaTex expression showing 4{c} to the power of 3
b A LaTex expression showing 2csquare root of 3
c A LaTex expression showing {c} to the power of 2 square root of 2
d A LaTex expression showing 4{c} to the power of 3 square root of 5
e A LaTex expression showing 3{c} to the power of 2 square root of 4
6
Simplify the radical
A LaTex expression showing square root of 3 times 3 times 11 times z times z times z times z
a A LaTex expression showing 4zsquare root of 9
b A LaTex expression showing {z} to the power of 4 square root of 13
c A LaTex expression showing 3{z} to the power of 2 square root of 11
d A LaTex expression showing 3{z} to the power of 3 square root of 9
e A LaTex expression showing {z} to the power of 2 square root of 12
7
Simplify the radical
A LaTex expression showing square root of 5 times 5 times 5 times n times n times n times n times n
a A LaTex expression showing 7{n} to the power of 3 square root of 8n
b A LaTex expression showing 5{n} to the power of 2 square root of 5n
c A LaTex expression showing {n} to the power of 4 square root of 2n
d A LaTex expression showing 2nsquare root of 3{n to the power of 3 }
e A LaTex expression showing 3{n} to the power of 3 square root of 8{n to the power of 2 }
8
Simplify the radical
A LaTex expression showing square root of 3 times 3 times 11 times m times m times m times m
a A LaTex expression showing 2msquare root of 8
b A LaTex expression showing 3{m} to the power of 2 square root of 11
c A LaTex expression showing 6msquare root of 14
d A LaTex expression showing 2{m} to the power of 3 square root of 12
e A LaTex expression showing msquare root of 12