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Radicals - Square - Simplify From Squared Factors, Values and Variables, Radical Remaining (Level 2)

This math topic focuses on simplifying radicals involving squared factors, values, and variables. It includes detailed practice problems that require extracting and simplifying squared factors from under the radical sign while leaving the non-squared parts inside the radical. Each problem presents an expression involving variables and constants under a radical, and students must identify the correct simplification with multiplicative constants and variable parts in and out of the radical. The problems progressively integrate more complex algebraic expressions, enhancing understanding of simplifying square roots and radicals.

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

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Square - Simplify From Squared Factors, Values and Variables, Radical Remaining

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Simplify the radical

22â‹…22â‹…3â‹…z2â‹…z2â‹…zâ‹…\sqrt{2^2\cdot 2^2\cdot 3\cdot z^2\cdot z^2\cdot z\cdot }

Radicals - Square - Simplify From Squared Factors, Values and Variables, Radical Remaining Worksheet

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Math worksheet on 'Radicals - Square - Simplify From Squared Factors, Values and Variables, Radical Remaining (Level 2)'. Part of a broader unit on 'Radicals - Simplifying Intro' Learn online: app.mobius.academy/math/units/radicals_simplifying_intro/
1
Simplify the radical
A LaTex expression showing square root of 2 to the power of 2 times 11 times x to the power of 2 times x to the power of 2 times
a A LaTex expression showing 5{x} to the power of 3 square root of 8
b A LaTex expression showing {x} to the power of 2 square root of 13
c A LaTex expression showing {x} to the power of 4 square root of 14
d A LaTex expression showing xsquare root of 10
e A LaTex expression showing 4{x} to the power of 4 square root of 11
f A LaTex expression showing 2{x} to the power of 2 square root of 11
2
Simplify the radical
A LaTex expression showing square root of 3 times 5 to the power of 2 times c to the power of 2 times c to the power of 2 times
a A LaTex expression showing 7csquare root of 4
b A LaTex expression showing 5{c} to the power of 2 square root of 3
c A LaTex expression showing 7c
d A LaTex expression showing 2{c} to the power of 4 square root of 5
e A LaTex expression showing 5{c} to the power of 4
f A LaTex expression showing 8csquare root of 2
3
Simplify the radical
A LaTex expression showing square root of 2 to the power of 2 times 3 times y to the power of 2 times y to the power of 2 times
a A LaTex expression showing 3ysquare root of 5
b A LaTex expression showing 2{y} to the power of 3 square root of 6
c A LaTex expression showing 3y
d A LaTex expression showing {y} to the power of 3 square root of 2
e A LaTex expression showing {y} to the power of 4
f A LaTex expression showing 2{y} to the power of 2 square root of 3
4
Simplify the radical
A LaTex expression showing square root of 3 to the power of 2 times 3 times r to the power of 2 times r to the power of 2 times r times
a A LaTex expression showing {r} to the power of 2 square root of 4r
b A LaTex expression showing 3{r} to the power of 2 square root of 3r
c A LaTex expression showing 3rsquare root of {r to the power of 3 }
d A LaTex expression showing {r} to the power of 3 square root of 2r
e A LaTex expression showing {r} to the power of 2 square root of 3{r to the power of 3 }
f A LaTex expression showing rsquare root of 5{r to the power of 2 }
5
Simplify the radical
A LaTex expression showing square root of 2 to the power of 2 times 11 times y to the power of 2 times y to the power of 2 times
a A LaTex expression showing 2{y} to the power of 2 square root of 11
b A LaTex expression showing {y} to the power of 3 square root of 7
c A LaTex expression showing ysquare root of 13
d A LaTex expression showing 4{y} to the power of 2 square root of 9
e A LaTex expression showing {y} to the power of 3 square root of 8
f A LaTex expression showing {y} to the power of 2 square root of 8
6
Simplify the radical
A LaTex expression showing square root of 2 to the power of 2 times 2 to the power of 2 times 5 times p to the power of 2 times p to the power of 2 times
a A LaTex expression showing {p} to the power of 3 square root of 7
b A LaTex expression showing 7{p} to the power of 3 square root of 3
c A LaTex expression showing 7{p} to the power of 2 square root of 7
d A LaTex expression showing 4{p} to the power of 2 square root of 5
e A LaTex expression showing 6psquare root of 8
f A LaTex expression showing psquare root of 4
7
Simplify the radical
A LaTex expression showing square root of 3 times 5 to the power of 2 times x to the power of 2 times
a A LaTex expression showing xsquare root of 3
b A LaTex expression showing 2{x} to the power of 2 square root of 4
c A LaTex expression showing 5xsquare root of 3
d A LaTex expression showing 3x
e A LaTex expression showing xsquare root of 4
f A LaTex expression showing 6xsquare root of 2