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Radicals - 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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Square - Simplifying from Factors, Values and Variables, Nothing Remaining

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Simplify the radical

3â‹…3â‹…câ‹…c\sqrt{3\cdot 3\cdot c\cdot c}

Radicals - Square - Simplifying from Factors, Values and Variables, Nothing Remaining Worksheet

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Math worksheet on 'Radicals - Square - Simplifying from Factors, Values and Variables, Nothing Remaining (Level 1)'. 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 5 times 5 times n times n
a A LaTex expression showing 2nsquare root of 3
b A LaTex expression showing 4{n} to the power of 2 square root of 3
c A LaTex expression showing 5nsquare root of 3
d A LaTex expression showing 6n
e A LaTex expression showing 6{n} to the power of 3
f A LaTex expression showing 5n
2
Simplify the radical
A LaTex expression showing square root of 3 times 3 times d times d
a A LaTex expression showing 3d
b A LaTex expression showing d
c A LaTex expression showing {d} to the power of 3 square root of 4
d A LaTex expression showing 2{d} to the power of 3 square root of 2
e A LaTex expression showing 5d
f A LaTex expression showing 2{d} to the power of 3 square root of 4
3
Simplify the radical
A LaTex expression showing square root of 2 times 2 times 2 times 2 times y times y
a A LaTex expression showing 3ysquare root of 2
b A LaTex expression showing 3y
c A LaTex expression showing 4y
d A LaTex expression showing 3{y} to the power of 3
e A LaTex expression showing ysquare root of 3
f A LaTex expression showing 7y
4
Simplify the radical
A LaTex expression showing square root of 3 times 3 times b times b
a A LaTex expression showing 4{b} to the power of 2 square root of 4
b A LaTex expression showing {b} to the power of 3
c A LaTex expression showing {b} to the power of 2
d A LaTex expression showing {b} to the power of 2 square root of 3
e A LaTex expression showing 5b
f A LaTex expression showing 3b
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 3{d} to the power of 3
b A LaTex expression showing 4d
c A LaTex expression showing 7{d} to the power of 3 square root of 2
d A LaTex expression showing 3dsquare root of 3
e A LaTex expression showing 4{d} to the power of 3
f A LaTex expression showing 2d
6
Simplify the radical
A LaTex expression showing square root of 3 times 3 times c times c
a A LaTex expression showing 5c
b A LaTex expression showing {c} to the power of 3
c A LaTex expression showing c
d A LaTex expression showing 6c
e A LaTex expression showing {c} to the power of 3 square root of 2
f A LaTex expression showing 3c
7
Simplify the radical
A LaTex expression showing square root of 2 times 2 times p times p
a A LaTex expression showing 4p
b A LaTex expression showing p
c A LaTex expression showing {p} to the power of 3 square root of 2
d A LaTex expression showing 2psquare root of 2
e A LaTex expression showing psquare root of 3
f A LaTex expression showing 2p