What is 3sqrt(-1000) ?

The solution to 3sqrt(-1000) is 30sqrt(10)i

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simplify 3sqrt(-1000)

simplify

3 - 1000

3010 i

Solution steps

3 - 1000

Prime factorization of

1000 : 2^{3} \cdot 5^{3}

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

Apply exponent rule:

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

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

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

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

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

Apply radical rule:

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

2^{2} = 2

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

Apply radical rule:

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

5^{2} = 5

= 3 \cdot 2 \cdot 5 - 2 \cdot 5

Multiply the numbers:

2 \cdot 5 = 10

= 3 \cdot 10 - 10

Multiply the numbers:

3 \cdot 10 = 30

= 30 - 10

Apply radical rule:

- a = a - 1

- 10 = 10 - 1

= 3010 - 1

Apply imaginary number rule:

- 1 = i

= 3010 i

\frac{1}{3} + \frac{1}{2}

1 + \frac{1}{x + 2}

3^{2} + (33)^{2}

\frac{2}{7} \div 2