Radical

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

325n\sqrt{3^2\cdot 5\cdot n}

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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 Practice' Learn online: app.mobius.academy/math/units/radicals_simplifying_practice/
1
Simplify the radical
A LaTex expression showing square root of 3 to the power of 2 times 3 times b to the power of 2 times b times
a A LaTex expression showing 3bsquare root of 4b
b A LaTex expression showing 3bsquare root of 3b
c A LaTex expression showing 4bsquare root of b
d A LaTex expression showing 6{b} to the power of 2 square root of b
e A LaTex expression showing 4{b} to the power of 3 square root of b
f A LaTex expression showing bsquare root of 6b
2
Simplify the radical
A LaTex expression showing square root of 3 to the power of 2 times 7 times m to the power of 2 times
a A LaTex expression showing {m} to the power of 2 square root of 6
b A LaTex expression showing 3msquare root of 9
c A LaTex expression showing msquare root of 4
d A LaTex expression showing {m} to the power of 2 square root of 8
e A LaTex expression showing 3msquare root of 10
f A LaTex expression showing 3msquare root of 7
3
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 rsquare root of 5{r to the power of 2 }
b A LaTex expression showing {r} to the power of 2 square root of 3{r to the power of 3 }
c A LaTex expression showing 3rsquare root of {r to the power of 3 }
d A LaTex expression showing 3{r} to the power of 2 square root of 3r
e A LaTex expression showing {r} to the power of 3 square root of 2r
f A LaTex expression showing {r} to the power of 2 square root of 4r
4
Simplify the radical
A LaTex expression showing square root of 2 to the power of 2 times 2 to the power of 2 times 3 times z to the power of 2 times z to the power of 2 times z times
a A LaTex expression showing 6zsquare root of z
b A LaTex expression showing {z} to the power of 3 square root of {z to the power of 2 }
c A LaTex expression showing 4zsquare root of z
d A LaTex expression showing 4{z} to the power of 2 square root of 3z
e A LaTex expression showing 4{z} to the power of 2 square root of z
f A LaTex expression showing {z} to the power of 3 square root of 6z
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 5 times p to the power of 2 times p to the power of 2 times
a A LaTex expression showing 6psquare root of 8
b A LaTex expression showing 4{p} to the power of 2 square root of 5
c A LaTex expression showing 7{p} to the power of 3 square root of 3
d A LaTex expression showing {p} to the power of 3 square root of 7
e A LaTex expression showing psquare root of 4
f A LaTex expression showing 7{p} to the power of 2 square root of 7
6
Simplify the radical
A LaTex expression showing square root of 2 to the power of 2 times 2 times p to the power of 2 times p to the power of 2 times
a A LaTex expression showing psquare root of 4
b A LaTex expression showing 2p
c A LaTex expression showing 5{p} to the power of 3
d A LaTex expression showing 2{p} to the power of 4
e A LaTex expression showing {p} to the power of 2 square root of 5
f A LaTex expression showing 2{p} to the power of 2 square root of 2
7
Simplify the radical
A LaTex expression showing square root of 2 times 5 to the power of 2 times b to the power of 2 times b to the power of 2 times b times
a A LaTex expression showing 4{b} to the power of 4 square root of {b to the power of 3 }
b A LaTex expression showing 5{b} to the power of 2 square root of 2b
c A LaTex expression showing 6{b} to the power of 3 square root of b
d A LaTex expression showing 7bsquare root of b
e A LaTex expression showing 6bsquare root of b
f A LaTex expression showing 3{b} to the power of 3 square root of {b to the power of 3 }