What is 2sqrt(-125) ?

The solution to 2sqrt(-125) is 10sqrt(5)i

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simplify 2sqrt(-125)

simplify

2 - 125

105 i

Solution steps

2 - 125

Prime factorization of

125 : 5^{3}

= 2 - 5^{3}

Apply exponent rule:

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

- 5^{3} = - 5^{2} \cdot 5

= 2 - 5^{2} \cdot 5

Apply radical rule:

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

- 5^{2} \cdot 5 = 5^{2} - 5

= 2 5^{2} - 5

Apply radical rule:

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

5^{2} = 5

= 2 \cdot 5 - 5

Multiply the numbers:

2 \cdot 5 = 10

= 10 - 5

Apply radical rule:

- a = a - 1

- 5 = 5 - 1

= 105 - 1

Apply imaginary number rule:

- 1 = i

= 105 i

\frac{2 + 3 i}{5 - i}

0.0121

0.0169

\frac{x}{2} + \frac{3}{2}

8 a b^{5} 27 a^{7} b