What is 5sqrt(-243) ?

The solution to 5sqrt(-243) is 45sqrt(3)i

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simplify 5sqrt(-243)

simplify

5 - 243

453 i

Solution steps

5 - 243

Prime factorization of

243 : 3^{5}

= 5 - 3^{5}

Apply exponent rule:

a^{b + c} = a^{b} \cdot a^{c}

- 3^{5} = - 3^{4} \cdot 3

= 5 - 3^{4} \cdot 3

Apply radical rule:

ab = a b, a \geq 0, b \geq 0

- 3^{4} \cdot 3 = 3^{4} - 3

= 5 3^{4} - 3

3^{4} = 9

= 5 \cdot 9 - 3

Multiply the numbers:

5 \cdot 9 = 45

= 45 - 3

Apply radical rule:

- a = a - 1

- 3 = 3 - 1

= 453 - 1

Apply imaginary number rule:

- 1 = i

= 453 i

\frac{( x + 1 ) ^{2} - 1}{x}

\frac{6}{5} - \frac{1}{5}

\frac{360}{40}

(\frac{3}{4})^{\frac{- 1}{2}}

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