Issolvi sqrt{-2}+9sqrt{-8}-4sqrt{-16}

$$\sqrt { - 2 } + 9 \sqrt { - 8 } - 4 \sqrt { - 16 }$$

Evalwa (complex solution)

$$19\sqrt{2}i-16i\approx 10.870057685i$$

Passi tas-Soluzzjonijiet

Iffattura -2=2\left(-1\right). Erġa' ikteb l-għerq kwadrat tal-prodott \sqrt{2\left(-1\right)} bħala l-prodott tal-għeruq kwadrati \sqrt{2}\sqrt{-1}. Skont id-definizzjoni, l-għerq kwadrat ta' -1 huwa i.

$$\sqrt{2}i+9\sqrt{-8}-4\sqrt{-16}$$

Iffattura -8=\left(2i\right)^{2}\times 2. Erġa' ikteb l-għerq kwadrat tal-prodott \sqrt{\left(2i\right)^{2}\times 2} bħala l-prodott tal-għeruq kwadrati \sqrt{\left(2i\right)^{2}}\sqrt{2}. Ħu l-għerq kwadrat ta' \left(2i\right)^{2}.

$$\sqrt{2}i+9\times \left(2i\right)\sqrt{2}-4\sqrt{-16}$$

Immultiplika 9 u 2i biex tikseb 18i.

$$\sqrt{2}i+18i\sqrt{2}-4\sqrt{-16}$$

Ikkombina \sqrt{2}i u 18i\sqrt{2} biex tikseb 19i\sqrt{2}.

$$19i\sqrt{2}-4\sqrt{-16}$$

Ikkalkula l-għerq kwadrat ta' -16 u ikseb 4i.

$$19i\sqrt{2}-4\times \left(4i\right)$$

Immultiplika -4 u 4i biex tikseb -16i.

$$19i\sqrt{2}-16i$$

Parti Reali (complex solution)

$$0$$

Evalwa

$$\text{Indeterminate}$$