Radical

Square - Simplify From Squared Factors, Values and Variables, Radical Remaining (Level 1)

This math topic focuses on simplifying radicals that contain squared factors, numerical values, and variables while leaving some radicals remaining. It involves practicing skills on extracting and simplifying square roots from expressions with squared terms and variables, distinguishing simplified radical forms, and correctly applying basic algebraic rules to reduce complex radical expressions. These problems enhance understanding of manipulating terms under the square root and applying exponent rules to simplify expressions, which are crucial skills in algebra. Each question offers multiple answer choices for students to verify the correctness of their simplification process.

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

232b\sqrt{2\cdot 3^2\cdot b}

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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 1)'. 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 2 to the power of 2 times 7 times r to the power of 2 times r times
a A LaTex expression showing {r} to the power of 3 square root of 8r
b A LaTex expression showing rsquare root of 10{r to the power of 2 }
c A LaTex expression showing 4{r} to the power of 3 square root of 10{r to the power of 2 }
d A LaTex expression showing 5rsquare root of 8r
e A LaTex expression showing 3rsquare root of 3r
f A LaTex expression showing 2rsquare root of 7r
2
Simplify the radical
A LaTex expression showing square root of 2 to the power of 2 times 3 times d to the power of 2 times d times
a A LaTex expression showing 2dsquare root of 3d
b A LaTex expression showing 5dsquare root of {d to the power of 2 }
c A LaTex expression showing 5{d} to the power of 3 square root of 4d
d A LaTex expression showing 3dsquare root of 6d
e A LaTex expression showing 2{d} to the power of 3 square root of d
f A LaTex expression showing {d} to the power of 2 square root of 6{d to the power of 3 }
3
Simplify the radical
A LaTex expression showing square root of 3 times 5 to the power of 2 times n to the power of 2 times n times
a A LaTex expression showing 5nsquare root of 2{n to the power of 2 }
b A LaTex expression showing 6{n} to the power of 3 square root of {n to the power of 3 }
c A LaTex expression showing 5nsquare root of 3n
d A LaTex expression showing 3{n} to the power of 2 square root of 6n
e A LaTex expression showing 4{n} to the power of 3 square root of 3n
f A LaTex expression showing 7nsquare root of {n to the power of 2 }
4
Simplify the radical
A LaTex expression showing square root of 2 to the power of 2 times 7 times y times
a A LaTex expression showing 2square root of 10{y to the power of 3 }
b A LaTex expression showing 5square root of 5{y to the power of 3 }
c A LaTex expression showing 4square root of 6{y to the power of 2 }
d A LaTex expression showing square root of 10y
e A LaTex expression showing 2square root of 7{y to the power of 3 }
f A LaTex expression showing 2square root of 7y
5
Simplify the radical
A LaTex expression showing square root of 2 times 3 to the power of 2 times d to the power of 2 times
a A LaTex expression showing 5{d} to the power of 3 square root of 3
b A LaTex expression showing d
c A LaTex expression showing 4{d} to the power of 3
d A LaTex expression showing 2{d} to the power of 2 square root of 4
e A LaTex expression showing 3dsquare root of 2
f A LaTex expression showing 5dsquare root of 2
6
Simplify the radical
A LaTex expression showing square root of 5 to the power of 2 times 7 times p to the power of 2 times p times
a A LaTex expression showing 3{p} to the power of 3 square root of 7p
b A LaTex expression showing 4{p} to the power of 3 square root of 9p
c A LaTex expression showing 3psquare root of 8p
d A LaTex expression showing 3psquare root of 5p
e A LaTex expression showing 5psquare root of 7p
f A LaTex expression showing 6psquare root of 9{p to the power of 3 }
7
Simplify the radical
A LaTex expression showing square root of 2 to the power of 2 times 5 times z to the power of 2 times z times
a A LaTex expression showing 4zsquare root of 7{z to the power of 2 }
b A LaTex expression showing 4{z} to the power of 2 square root of 4{z to the power of 3 }
c A LaTex expression showing 4{z} to the power of 3 square root of 6{z to the power of 2 }
d A LaTex expression showing 2zsquare root of 5z
e A LaTex expression showing {z} to the power of 2 square root of 8z
f A LaTex expression showing {z} to the power of 2 square root of 3{z to the power of 2 }