The solution to 2sqrt(-40) is 4sqrt(10)i

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simplify 2sqrt(-40)

Solution

simplify

2 - 40

410 i

Solution steps

2 - 40

Prime factorization of

40 : 2^{3} \cdot 5

= 2 - 2^{3} \cdot 5

Apply exponent rule:

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

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

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

Apply radical rule:

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

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

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

Apply radical rule:

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

2^{2} = 2

= 2 \cdot 2 - 2 \cdot 5

Multiply the numbers:

2 \cdot 5 = 10

= 2 \cdot 2 - 10

Multiply the numbers:

2 \cdot 2 = 4

= 4 - 10

Apply radical rule:

- a = a - 1

- 10 = 10 - 1

= 410 - 1

Apply imaginary number rule:

- 1 = i

= 410 i

\frac{12 x ^{6}}{42 x ^{4}}

x^{4} - 14 x^{3} + 13 x^{2}

(27 x)^{\frac{1}{3}}

\frac{5 x ^{6} y}{25 x ^{3} y ^{4}}

s^{2} - 14 s + 33