Square - Simplifying from Factors, Values and Variables, Nothing Remaining (Level 2)

This math topic focuses on simplifying square radicals involving factors, values, and variables. It involves problems where students practice simplifying expressions under the radical to their simplest form. Each problem presents a radical expression containing repeated factors and variables, and students must simplify these using radical laws and algebraic manipulations. The skills practiced include understanding the properties of exponents and simplifying expressions within square roots.

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, Nothing Remaining Worksheet

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Radicals - Square - Simplifying from Factors, Values and Variables, Nothing Remaining
1
Simplify the radical
A LaTex expression showing square root of 2 times 2 times y times y times y times y
a A LaTex expression showing {y} to the power of 2
b A LaTex expression showing 5{y} to the power of 3 square root of 4
c A LaTex expression showing 2{y} to the power of 2
d A LaTex expression showing y
2
Simplify the radical
A LaTex expression showing square root of 3 times 3 times z times z times z times z
a A LaTex expression showing 5{z} to the power of 3 square root of 4
b A LaTex expression showing 5{z} to the power of 2 square root of 3
c A LaTex expression showing 3{z} to the power of 2
d A LaTex expression showing 3z
e A LaTex expression showing zsquare root of 2
3
Simplify the radical
A LaTex expression showing square root of 3 times 3 times d times d times d times d
a A LaTex expression showing 5d
b A LaTex expression showing 4{d} to the power of 3 square root of 4
c A LaTex expression showing 4{d} to the power of 2
d A LaTex expression showing 3{d} to the power of 2
e A LaTex expression showing d
4
Simplify the radical
A LaTex expression showing square root of 3 times 3 times x times x
a A LaTex expression showing 3xsquare root of 4
b A LaTex expression showing 3xsquare root of 2
c A LaTex expression showing 3x
d A LaTex expression showing 2{x} to the power of 2 square root of 4
e A LaTex expression showing 6{x} to the power of 3 square root of 3
5
Simplify the radical
A LaTex expression showing square root of 2 times 2 times 2 times 2 times p times p times p times p
a A LaTex expression showing 6{p} to the power of 2
b A LaTex expression showing 2p
c A LaTex expression showing 4{p} to the power of 2
d A LaTex expression showing 6p
e A LaTex expression showing 7{p} to the power of 3
6
Simplify the radical
A LaTex expression showing square root of 5 times 5 times m times m
a A LaTex expression showing 8msquare root of 4
b A LaTex expression showing 8m
c A LaTex expression showing 5m
d A LaTex expression showing {m} to the power of 3
7
Simplify the radical
A LaTex expression showing square root of 2 times 2 times p times p
a A LaTex expression showing 2p
b A LaTex expression showing 5{p} to the power of 2 square root of 3
c A LaTex expression showing psquare root of 4
d A LaTex expression showing p
e A LaTex expression showing psquare root of 2
8
Simplify the radical
A LaTex expression showing square root of 5 times 5 times b times b
a A LaTex expression showing 5{b} to the power of 2 square root of 4
b A LaTex expression showing 6bsquare root of 3
c A LaTex expression showing 5b
d A LaTex expression showing 3{b} to the power of 3
e A LaTex expression showing b