Rewriting Roots (Level 4)

This math topic focuses on practicing complex numbers, specifically rewriting roots as complex numbers and simplifying radicals. Each problem presents a unique expression involving a square root of a negative product, which needs to be expressed in terms of complex numbers (using the imaginary unit \(i\)). It enhances understanding of the fundamental concepts of complex numbers and the manipulation of expressions involving powers and roots. The problems progressively build skills in simplifying and rewriting complex expressions in clearer forms and algebraic manipulation involving imaginary numbers.

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

63bp3\sqrt{-63b{p}^{3}}

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Complex Numbers - Rewriting Roots Worksheet

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Math worksheet on 'Complex Numbers - Rewriting Roots (Level 4)'. 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 -48{z to the power of 4 {y} to the power of 4 }
a A LaTex expression showing z{y} to the power of 4 isquare root of 3
b A LaTex expression showing zyi
c A LaTex expression showing 2{z} to the power of 4 {y} to the power of 3 isquare root of 4
d A LaTex expression showing 3zyisquare root of 5
e A LaTex expression showing 7{z} to the power of 3 yisquare root of 4
f A LaTex expression showing 4{z} to the power of 2 {y} to the power of 2 isquare root of 3
2
Rewrite the root as a complex number and simplify all radicals
A LaTex expression showing square root of -176xy
a A LaTex expression showing 6isquare root of 12xy
b A LaTex expression showing 6isquare root of 11xy
c A LaTex expression showing 4isquare root of 11xy
d A LaTex expression showing 3isquare root of 8xy
e A LaTex expression showing 6isquare root of 14xy
f A LaTex expression showing 3isquare root of 11xy
3
Rewrite the root as a complex number and simplify all radicals
A LaTex expression showing square root of -20{r to the power of 3 {p} to the power of 4 }
a A LaTex expression showing 2r{p} to the power of 2 isquare root of 5r
b A LaTex expression showing 4r{p} to the power of 3 isquare root of 5r
c A LaTex expression showing rpisquare root of 5{r to the power of 2 }
d A LaTex expression showing 2{r} to the power of 3 pisquare root of r
e A LaTex expression showing {r} to the power of 3 {p} to the power of 3 isquare root of 4r
f A LaTex expression showing {r} to the power of 3 pisquare root of 4{r to the power of 2 }
4
Rewrite the root as a complex number and simplify all radicals
A LaTex expression showing square root of -18{z to the power of 3 {x} to the power of 4 }
a A LaTex expression showing {z} to the power of 2 xisquare root of z
b A LaTex expression showing 3{z} to the power of 2 xisquare root of {z to the power of 3 }
c A LaTex expression showing 2zxisquare root of {z to the power of 2 }
d A LaTex expression showing 6{z} to the power of 3 xisquare root of {z to the power of 3 }
e A LaTex expression showing {z} to the power of 3 {x} to the power of 2 isquare root of 3z
f A LaTex expression showing 3z{x} to the power of 2 isquare root of 2z
5
Rewrite the root as a complex number and simplify all radicals
A LaTex expression showing square root of -28d{c to the power of 4 }
a A LaTex expression showing 5{c} to the power of 3 isquare root of 3d
b A LaTex expression showing 2cisquare root of 5d
c A LaTex expression showing cisquare root of 10{d to the power of 2 }
d A LaTex expression showing 4{c} to the power of 2 isquare root of 6{d to the power of 2 }
e A LaTex expression showing {c} to the power of 3 isquare root of 7{d to the power of 3 }
f A LaTex expression showing 2{c} to the power of 2 isquare root of 7d
6
Rewrite the root as a complex number and simplify all radicals
A LaTex expression showing square root of -20{z to the power of 3 r}
a A LaTex expression showing 3{z} to the power of 3 isquare root of 6z{r to the power of 3 }
b A LaTex expression showing {z} to the power of 2 isquare root of 6{z to the power of 3 {r} to the power of 3 }
c A LaTex expression showing zisquare root of z{r to the power of 2 }
d A LaTex expression showing zisquare root of {z to the power of 3 {r} to the power of 2 }
e A LaTex expression showing 2zisquare root of 5zr
f A LaTex expression showing 3zisquare root of 7zr
7
Rewrite the root as a complex number and simplify all radicals
A LaTex expression showing square root of -20{n to the power of 4 {x} to the power of 3 }
a A LaTex expression showing 2nxisquare root of 4x
b A LaTex expression showing n{x} to the power of 2 isquare root of 7x
c A LaTex expression showing 2{n} to the power of 2 xisquare root of 5x
d A LaTex expression showing 2{n} to the power of 3 {x} to the power of 3 isquare root of 3{x to the power of 2 }
e A LaTex expression showing 4{n} to the power of 4 xisquare root of 4x
f A LaTex expression showing 5{n} to the power of 2 xisquare root of 8x