Square - Simplifying from Factors, Values and Variables, Radical Remaining (Level 1)

This topic covers simplifying square roots involving factors, values, and variables, with a radical remaining. Problems require extracting and simplifying square roots from algebraic expressions. The questions present multiple-choice answers, focusing on simplification techniques such as factoring out perfect squares and handling variables within the radical. This emphasizes foundational skills in manipulating radicals, which is crucial for higher-level algebra.

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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 2 times 2 times 2 times 2 times 2 times d times d times d
a A LaTex expression showing 6{d} to the power of 2 square root of 3d
b A LaTex expression showing 3{d} to the power of 3 square root of 5d
c A LaTex expression showing 4dsquare root of 2d
d A LaTex expression showing 5dsquare root of 5d
e A LaTex expression showing 7dsquare root of 3d
2
Simplify the radical
A LaTex expression showing square root of 2 times 2 times 2 times n times n times n
a A LaTex expression showing 2nsquare root of 5{n to the power of 2 }
b A LaTex expression showing 2nsquare root of 2n
c A LaTex expression showing nsquare root of 5n
d A LaTex expression showing 4nsquare root of n
3
Simplify the radical
A LaTex expression showing square root of 2 times 5 times 5 times m times m times m
a A LaTex expression showing {m} to the power of 2 square root of 3m
b A LaTex expression showing 7{m} to the power of 3 square root of 3m
c A LaTex expression showing 8msquare root of 3{m to the power of 3 }
d A LaTex expression showing 5msquare root of 2m
e A LaTex expression showing 4{m} to the power of 2 square root of 3m
4
Simplify the radical
A LaTex expression showing square root of 2 times 2 times 3 times n
a A LaTex expression showing square root of n
b A LaTex expression showing 5square root of 4n
c A LaTex expression showing 2square root of 3n
d A LaTex expression showing square root of 4n
e A LaTex expression showing square root of 5{n to the power of 2 }
5
Simplify the radical
A LaTex expression showing square root of 2 times 2 times 5 times p times p times p
a A LaTex expression showing 5psquare root of 3{p to the power of 2 }
b A LaTex expression showing 2psquare root of 5p
c A LaTex expression showing {p} to the power of 3 square root of 5p
d A LaTex expression showing psquare root of 4p
6
Simplify the radical
A LaTex expression showing square root of 2 times 2 times 5 times d times d times d
a A LaTex expression showing 5dsquare root of 7{d to the power of 2 }
b A LaTex expression showing 5dsquare root of 4{d to the power of 2 }
c A LaTex expression showing 5{d} to the power of 2 square root of 6{d to the power of 2 }
d A LaTex expression showing 2dsquare root of 5d
e A LaTex expression showing {d} to the power of 3 square root of 8d
7
Simplify the radical
A LaTex expression showing square root of 2 times 2 times 2 times r times r times r
a A LaTex expression showing 4{r} to the power of 2 square root of r
b A LaTex expression showing {r} to the power of 2 square root of {r to the power of 2 }
c A LaTex expression showing rsquare root of {r to the power of 3 }
d A LaTex expression showing rsquare root of 5r
e A LaTex expression showing 2rsquare root of 2r
8
Simplify the radical
A LaTex expression showing square root of 2 times 2 times 2 times 2 times 2 times r times r
a A LaTex expression showing 5rsquare root of 2
b A LaTex expression showing 4rsquare root of 2
c A LaTex expression showing {r} to the power of 2 square root of 3
d A LaTex expression showing 7rsquare root of 2
e A LaTex expression showing {r} to the power of 3 square root of 2