Square - Simplify From Squared Factors, Values and Variables, Nothing Remaining (Level 1)

This math topic focuses on simplifying square radicals involving squared factors, values, and variables, ensuring nothing remains in the radical. It is an introduction to simplifying radicals, covering the fundamental skills needed to simplify expressions under a square root, especially when variables and constants are raised to the power of two. Each problem presents a radical expression and multiple choice answers, requiring students to identify the correct simplified form. The problems gradually build on complexity, reinforcing the understanding of how to handle square roots of squares in algebraic expressions.

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

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Radicals - Square - Simplify From Squared Factors, Values and Variables, Nothing Remaining Worksheet

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Radicals - Square - Simplify From Squared Factors, Values and Variables, Nothing Remaining
1
Simplify the radical
A LaTex expression showing square root of 3 to the power of 2 times r to the power of 2
a A LaTex expression showing 4r
b A LaTex expression showing 3{r} to the power of 3 square root of 4
c A LaTex expression showing r
d A LaTex expression showing 6r
e A LaTex expression showing 3r
2
Simplify the radical
A LaTex expression showing square root of 5 to the power of 2 times y to the power of 2
a A LaTex expression showing 5{y} to the power of 2 square root of 4
b A LaTex expression showing 5y
c A LaTex expression showing 3ysquare root of 2
d A LaTex expression showing y
e A LaTex expression showing 7{y} to the power of 2
3
Simplify the radical
A LaTex expression showing square root of 5 to the power of 2 times d to the power of 2
a A LaTex expression showing 5d
b A LaTex expression showing 6{d} to the power of 3
c A LaTex expression showing 7dsquare root of 3
d A LaTex expression showing 4{d} to the power of 2
e A LaTex expression showing 2{d} to the power of 2 square root of 4
4
Simplify the radical
A LaTex expression showing square root of 2 to the power of 2 times n to the power of 2
a A LaTex expression showing 2n
b A LaTex expression showing 4{n} to the power of 2
c A LaTex expression showing 4n
d A LaTex expression showing n
5
Simplify the radical
A LaTex expression showing square root of 2 to the power of 2 times 2 to the power of 2 times x to the power of 2
a A LaTex expression showing 2{x} to the power of 3
b A LaTex expression showing 3{x} to the power of 3
c A LaTex expression showing 2xsquare root of 3
d A LaTex expression showing 6{x} to the power of 2
e A LaTex expression showing 4x
6
Simplify the radical
A LaTex expression showing square root of 2 to the power of 2 times y to the power of 2
a A LaTex expression showing 2y
b A LaTex expression showing 5ysquare root of 2
c A LaTex expression showing {y} to the power of 3 square root of 4
d A LaTex expression showing 5ysquare root of 3
7
Simplify the radical
A LaTex expression showing square root of 5 to the power of 2 times r to the power of 2
a A LaTex expression showing 2rsquare root of 2
b A LaTex expression showing 7rsquare root of 2
c A LaTex expression showing rsquare root of 2
d A LaTex expression showing 5r
8
Simplify the radical
A LaTex expression showing square root of 2 to the power of 2 times z to the power of 2
a A LaTex expression showing 2z
b A LaTex expression showing 3{z} to the power of 2 square root of 4
c A LaTex expression showing 5z
d A LaTex expression showing z