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.

more
View

Complex Numbers - Rewriting Roots Worksheet

Mobius Math Academy logo
Complex Numbers - Rewriting Roots
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 isquare root of 9
b A LaTex expression showing isquare root of 5
c A LaTex expression showing 3isquare root of 3
d A LaTex expression showing 4isquare root of 7
e A LaTex expression showing isquare root of 10
f A LaTex expression showing 7isquare root of 8
2
Rewrite the root as a complex number and simplify all radicals
A LaTex expression showing square root of -125
a A LaTex expression showing 5isquare root of 5
b A LaTex expression showing 3isquare root of 8
c A LaTex expression showing 7isquare root of 5
d A LaTex expression showing 8isquare root of 8
e A LaTex expression showing 2isquare root of 5
f A LaTex expression showing 4isquare root of 8
3
Rewrite the root as a complex number and simplify all radicals
A LaTex expression showing square root of -275
a A LaTex expression showing 6isquare root of 10
b A LaTex expression showing 2isquare root of 12
c A LaTex expression showing 6isquare root of 12
d A LaTex expression showing 4isquare root of 14
e A LaTex expression showing 8isquare root of 7
f A LaTex expression showing 5isquare root of 11
4
Rewrite the root as a complex number and simplify all radicals
A LaTex expression showing square root of -18
a A LaTex expression showing 2isquare root of 4
b A LaTex expression showing 3i
c A LaTex expression showing isquare root of 3
d A LaTex expression showing 3isquare root of 2
e A LaTex expression showing 5i
f A LaTex expression showing 6i
5
Rewrite the root as a complex number and simplify all radicals
A LaTex expression showing square root of -45
a A LaTex expression showing 5i
b A LaTex expression showing 3isquare root of 5
c A LaTex expression showing isquare root of 5
d A LaTex expression showing 2i
e A LaTex expression showing 5isquare root of 3
f A LaTex expression showing 6isquare root of 6
6
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 12
b A LaTex expression showing isquare root of 7
c A LaTex expression showing 2isquare root of 11
d A LaTex expression showing 2isquare root of 12
e A LaTex expression showing isquare root of 14
f A LaTex expression showing 5isquare root of 11
7
Rewrite the root as a complex number and simplify all radicals
A LaTex expression showing square root of -63
a A LaTex expression showing 2isquare root of 9
b A LaTex expression showing 3isquare root of 7
c A LaTex expression showing isquare root of 8
d A LaTex expression showing isquare root of 7
e A LaTex expression showing isquare root of 5
f A LaTex expression showing isquare root of 6
8
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 isquare root of 3
c A LaTex expression showing 2isquare root of 3
d A LaTex expression showing 3i
e A LaTex expression showing 7i
f A LaTex expression showing 5isquare root of 2