The solution to 5sqrt(-8) is 10sqrt(2)i

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simplify 5sqrt(-8)

Solution

simplify

5 - 8

102 i

Solution steps

5 - 8

Prime factorization of

8 : 2^{3}

= 5 - 2^{3}

Apply exponent rule:

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

- 2^{3} = - 2^{2} \cdot 2

= 5 - 2^{2} \cdot 2

Apply radical rule:

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

- 2^{2} \cdot 2 = 2^{2} - 2

= 5 2^{2} - 2

Apply radical rule:

a^{2} = a, a \geq 0

2^{2} = 2

= 5 \cdot 2 - 2

Multiply the numbers:

5 \cdot 2 = 10

= 10 - 2

Apply radical rule:

- a = a - 1

- 2 = 2 - 1

= 102 - 1

Apply imaginary number rule:

- 1 = i

= 102 i

e^{3} = x

1000 = (0.000001) (256) (256 - x)

- 6 < \frac{2 x - 3}{4} < 2

∣ x - 2 ∣ \geq 7

\frac{1}{3} - 6