Square - Simplifying from Factors, Values and Variables, Nothing Remaining (Level 1)

This math topic focuses on simplifying square radicals involving factors, values, and variables, ensuring nothing remains under the radical. It encompasses a range of problems where learners need to apply simplification techniques to radicals containing multiple instances of numbers and variables. The questions are structured to provide multiple-choice answers, requiring students to select the correct simplified form of given radical expressions. The skill central to this topic is simplifying square roots by extracting perfect squares and simplifying terms which is crucial for algebraic proficiency.

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 2 times 2 times z times z
a A LaTex expression showing 4z
b A LaTex expression showing {z} to the power of 2
c A LaTex expression showing 3{z} to the power of 3
d A LaTex expression showing {z} to the power of 3
e A LaTex expression showing 2zsquare root of 3
2
Simplify the radical
A LaTex expression showing square root of 2 times 2 times n times n
a A LaTex expression showing nsquare root of 3
b A LaTex expression showing nsquare root of 2
c A LaTex expression showing nsquare root of 4
d A LaTex expression showing 2n
e A LaTex expression showing 3nsquare root of 2
3
Simplify the radical
A LaTex expression showing square root of 5 times 5 times z times z
a A LaTex expression showing 5z
b A LaTex expression showing 6zsquare root of 3
c A LaTex expression showing 7{z} to the power of 2
d A LaTex expression showing 2z
4
Simplify the radical
A LaTex expression showing square root of 2 times 2 times z times z
a A LaTex expression showing 2{z} to the power of 3
b A LaTex expression showing {z} to the power of 2
c A LaTex expression showing zsquare root of 2
d A LaTex expression showing 2z
e A LaTex expression showing 3{z} to the power of 2 square root of 4
5
Simplify the radical
A LaTex expression showing square root of 2 times 2 times 2 times 2 times d times d
a A LaTex expression showing d
b A LaTex expression showing 5d
c A LaTex expression showing 2{d} to the power of 3
d A LaTex expression showing 4d
6
Simplify the radical
A LaTex expression showing square root of 2 times 2 times d times d
a A LaTex expression showing {d} to the power of 3
b A LaTex expression showing 5dsquare root of 4
c A LaTex expression showing 3d
d A LaTex expression showing dsquare root of 4
e A LaTex expression showing 2d
7
Simplify the radical
A LaTex expression showing square root of 2 times 2 times 2 times 2 times b times b
a A LaTex expression showing 3bsquare root of 2
b A LaTex expression showing 5bsquare root of 2
c A LaTex expression showing 4b
d A LaTex expression showing 7b
8
Simplify the radical
A LaTex expression showing square root of 2 times 2 times 2 times 2 times n times n
a A LaTex expression showing 4n
b A LaTex expression showing 7n
c A LaTex expression showing 4{n} to the power of 2
d A LaTex expression showing {n} to the power of 2
e A LaTex expression showing 5{n} to the power of 3 square root of 2