Square - Simplify From Squared Factors, Values only, Radical Remaining (Level 3)

This math topic focuses on simplifying radicals, particularly extracting and simplifying square roots when squared factors are involved. The problems require identifying the perfect square factors within a radical and simplifying them to their integer values, while keeping any remaining non-square factors under the radical sign. This involves practicing extracting squares from expressions and understanding how to express the simplified result while still incorporating any leftover components from the original radical. The exercise is part of an introductory unit on simplifying radicals, providing foundational skills in dealing with radical 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 only, Radical Remaining Worksheet

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Radicals - Square - Simplify From Squared Factors, Values only, Radical Remaining
1
Simplify the radical
A LaTex expression showing square root of 2 times 3 to the power of 2
a A LaTex expression showing 6
b A LaTex expression showing square root of 3
c A LaTex expression showing 2square root of 2
d A LaTex expression showing 1
e A LaTex expression showing 3square root of 2
2
Simplify the radical
A LaTex expression showing square root of 2 to the power of 2 times 7
a A LaTex expression showing 2square root of 7
b A LaTex expression showing 3square root of 10
c A LaTex expression showing square root of 8
d A LaTex expression showing 3square root of 4
e A LaTex expression showing 5square root of 4
3
Simplify the radical
A LaTex expression showing square root of 2 to the power of 2 times 2 to the power of 2 times 11
a A LaTex expression showing 2square root of 10
b A LaTex expression showing 4square root of 11
c A LaTex expression showing 4square root of 10
d A LaTex expression showing 3square root of 8
e A LaTex expression showing 7square root of 14
4
Simplify the radical
A LaTex expression showing square root of 3 to the power of 2 times 3
a A LaTex expression showing square root of 6
b A LaTex expression showing 1
c A LaTex expression showing 3square root of 3
d A LaTex expression showing 5
e A LaTex expression showing square root of 3
5
Simplify the radical
A LaTex expression showing square root of 2 to the power of 2 times 3
a A LaTex expression showing 2square root of 3
b A LaTex expression showing square root of 4
c A LaTex expression showing square root of 2
d A LaTex expression showing square root of 3
e A LaTex expression showing 1
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 2
a A LaTex expression showing 4square root of 2
b A LaTex expression showing 6
c A LaTex expression showing 3
d A LaTex expression showing 5square root of 3
7
Simplify the radical
A LaTex expression showing square root of 5 to the power of 2 times 5
a A LaTex expression showing 7square root of 8
b A LaTex expression showing 3square root of 3
c A LaTex expression showing 5square root of 5
d A LaTex expression showing 4square root of 5
e A LaTex expression showing 5
8
Simplify the radical
A LaTex expression showing square root of 3 times 5 to the power of 2
a A LaTex expression showing 5square root of 3
b A LaTex expression showing 8square root of 2
c A LaTex expression showing 1
d A LaTex expression showing 4square root of 3
e A LaTex expression showing 4square root of 5