The solution to 4sqrt(-54) is 12sqrt(6)i

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simplify 4sqrt(-54)

Solution

simplify

4 - 54

126 i

Solution steps

4 - 54

Prime factorization of

54 : 2 \cdot 3^{3}

= 4 - 2 \cdot 3^{3}

Apply exponent rule:

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

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

= 4 - 2 \cdot 3^{2} \cdot 3

Apply radical rule:

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

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

= 4 3^{2} - 2 \cdot 3

Apply radical rule:

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

3^{2} = 3

= 4 \cdot 3 - 2 \cdot 3

Multiply the numbers:

2 \cdot 3 = 6

= 4 \cdot 3 - 6

Multiply the numbers:

4 \cdot 3 = 12

= 12 - 6

Apply radical rule:

- a = a - 1

- 6 = 6 - 1

= 126 - 1

Apply imaginary number rule:

- 1 = i

= 126 i

lo g_{10} (32)

- 4 - \frac{( 3 + 6 ^{2} )}{13} - 1^{2} \cdot (- 12)

+ \frac{4}{10} + \frac{3}{100}

7 \times 18

- 5 \times \frac{1}{5}