The solution to 3sqrt(-32) is 12sqrt(2)i

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simplify 3sqrt(-32)

Solution

simplify

3 - 32

122 i

Solution steps

3 - 32

Prime factorization of

32 : 2^{5}

= 3 - 2^{5}

Apply exponent rule:

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

- 2^{5} = - 2^{4} \cdot 2

= 3 - 2^{4} \cdot 2

Apply radical rule:

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

- 2^{4} \cdot 2 = 2^{4} - 2

= 3 2^{4} - 2

2^{4} = 4

= 3 \cdot 4 - 2

Multiply the numbers:

3 \cdot 4 = 12

= 12 - 2

Apply radical rule:

- a = a - 1

- 2 = 2 - 1

= 122 - 1

Apply imaginary number rule:

- 1 = i

= 122 i

\frac{1}{3} \times \frac{3}{2}

- 99

- \frac{1}{7} - 1

6 y^{2} + y - 1

\frac{13}{52} \times \frac{12}{51}