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Complex Number

Rewriting Roots (Level 3)

This math topic focuses on advanced manipulation of complex numbers, specifically the skill of rewriting square roots that contain negative radicands into complex number expressions. Students are encouraged to simplify such expressions and manage radicals effectively, integrating both imaginary units and variable exponents. The problems involve interpreting and transforming complex algebraic structures that include powers and roots into their simplified complex forms. This is an advanced exercise aimed at deepening understanding of complex numbers and their properties in the context of algebra.

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

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Rewriting Roots

Complete these online problems with 80% or 4 correct answers in a row. Results are immediate.

Rewrite the root as a complex number and simplify all radicals

−45c3\sqrt{-45{c}^{3}}

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Complex Numbers - Rewriting Roots Worksheet

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Math worksheet on 'Complex Numbers - Rewriting Roots (Level 3)'. 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 -125y
a A LaTex expression showing 5isquare root of 2{y to the power of 2 }
b A LaTex expression showing 5isquare root of 6{y to the power of 3 }
c A LaTex expression showing isquare root of 8y
d A LaTex expression showing 5isquare root of 5y
e A LaTex expression showing 4isquare root of 6y
f A LaTex expression showing 7isquare root of y
2
Rewrite the root as a complex number and simplify all radicals
A LaTex expression showing square root of -20{p to the power of 4 }
a A LaTex expression showing 2{p} to the power of 2 isquare root of 5
b A LaTex expression showing pisquare root of 6
c A LaTex expression showing 3{p} to the power of 2 isquare root of 3
d A LaTex expression showing 2{p} to the power of 4 isquare root of 8
e A LaTex expression showing pisquare root of 4
f A LaTex expression showing {p} to the power of 2 isquare root of 2
3
Rewrite the root as a complex number and simplify all radicals
A LaTex expression showing square root of -80{p to the power of 2 }
a A LaTex expression showing 3pi
b A LaTex expression showing 4pisquare root of 5
c A LaTex expression showing 2pisquare root of 4
d A LaTex expression showing 3pisquare root of 6
e A LaTex expression showing {p} to the power of 3 isquare root of 4
f A LaTex expression showing 2pi
4
Rewrite the root as a complex number and simplify all radicals
A LaTex expression showing square root of -175m
a A LaTex expression showing 3isquare root of 4m
b A LaTex expression showing 4isquare root of 4{m to the power of 2 }
c A LaTex expression showing 5isquare root of 7m
d A LaTex expression showing 8isquare root of 9m
e A LaTex expression showing 3isquare root of 10m
f A LaTex expression showing isquare root of 9m
5
Rewrite the root as a complex number and simplify all radicals
A LaTex expression showing square root of -112{x to the power of 4 }
a A LaTex expression showing 2xisquare root of 6
b A LaTex expression showing 3{x} to the power of 3 isquare root of 4
c A LaTex expression showing 2xisquare root of 4
d A LaTex expression showing 4{x} to the power of 4 isquare root of 4
e A LaTex expression showing 4{x} to the power of 2 isquare root of 7
f A LaTex expression showing 2{x} to the power of 4 isquare root of 4
6
Rewrite the root as a complex number and simplify all radicals
A LaTex expression showing square root of -63y
a A LaTex expression showing 3isquare root of 7y
b A LaTex expression showing 3isquare root of 9y
c A LaTex expression showing 6isquare root of 7y
d A LaTex expression showing 4isquare root of 6y
e A LaTex expression showing 5isquare root of 4{y to the power of 3 }
f A LaTex expression showing 5isquare root of 7y
7
Rewrite the root as a complex number and simplify all radicals
A LaTex expression showing square root of -32{d to the power of 3 }
a A LaTex expression showing 5{d} to the power of 3 isquare root of d
b A LaTex expression showing 3disquare root of 2d
c A LaTex expression showing 7{d} to the power of 2 isquare root of {d to the power of 3 }
d A LaTex expression showing 6{d} to the power of 3 isquare root of 2d
e A LaTex expression showing 4disquare root of 2d
f A LaTex expression showing 4{d} to the power of 3 isquare root of d