Rewriting Roots (Level 2)

This math topic focuses on complex numbers, specifically how to rewrite roots of negative numbers as complex numbers and simplifying radicals. It explores the application of the fundamental theorem of algebra where each question provides a negative radicand, challenging students to express it in terms of an imaginary unit 'i' by simplifying square roots. This skill is essential in understanding the properties and operations involving complex numbers. The exercises require converting square roots of negative integers into their simplest imaginary form.

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

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Rewriting Roots

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Rewrite the root as a complex number and simplify all radicals

80\sqrt{-80}

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Complex Numbers - Rewriting Roots Worksheet

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Math worksheet on 'Complex Numbers - Rewriting Roots (Level 2)'. Part of a broader unit on 'Complex Numbers' Learn online: app.mobius.academy/math/units/complex_numbers/
1
Rewrite the root as a complex number and simplify all radicals
A LaTex expression showing square root of -112
a A LaTex expression showing 4isquare root of 7
b A LaTex expression showing isquare root of 9
c A LaTex expression showing isquare root of 10
d A LaTex expression showing 7isquare root of 8
e A LaTex expression showing isquare root of 5
f A LaTex expression showing 3isquare root of 3
2
Rewrite the root as a complex number and simplify all radicals
A LaTex expression showing square root of -32
a A LaTex expression showing 3isquare root of 4
b A LaTex expression showing 2i
c A LaTex expression showing i
d A LaTex expression showing 6i
e A LaTex expression showing 4isquare root of 2
f A LaTex expression showing 5isquare root of 5
3
Rewrite the root as a complex number and simplify all radicals
A LaTex expression showing square root of -8
a A LaTex expression showing 5isquare root of 3
b A LaTex expression showing 2isquare root of 2
c A LaTex expression showing i
d A LaTex expression showing 2i
e A LaTex expression showing 5i
f A LaTex expression showing isquare root of 4
4
Rewrite the root as a complex number and simplify all radicals
A LaTex expression showing square root of -28
a A LaTex expression showing isquare root of 8
b A LaTex expression showing 3isquare root of 8
c A LaTex expression showing 2isquare root of 7
d A LaTex expression showing 5isquare root of 6
e A LaTex expression showing 3isquare root of 6
f A LaTex expression showing 3isquare root of 9
5
Rewrite the root as a complex number and simplify all radicals
A LaTex expression showing square root of -20
a A LaTex expression showing 5isquare root of 7
b A LaTex expression showing 2isquare root of 5
c A LaTex expression showing isquare root of 7
d A LaTex expression showing i
e A LaTex expression showing 3i
f A LaTex expression showing 5isquare root of 2
6
Rewrite the root as a complex number and simplify all radicals
A LaTex expression showing square root of -50
a A LaTex expression showing isquare root of 5
b A LaTex expression showing 2isquare root of 3
c A LaTex expression showing 5isquare root of 2
d A LaTex expression showing 3i
e A LaTex expression showing 7i
f A LaTex expression showing isquare root of 3
7
Rewrite the root as a complex number and simplify all radicals
A LaTex expression showing square root of -44
a A LaTex expression showing isquare root of 7
b A LaTex expression showing isquare root of 14
c A LaTex expression showing isquare root of 12
d A LaTex expression showing 2isquare root of 11
e A LaTex expression showing 2isquare root of 12
f A LaTex expression showing 5isquare root of 11