Issolvi 2*sqrt{49-2}left(6+2sqrt{3}+3sqrt{2}-sqrt{9}-sqrt{12}-sqrt{18}right)

$$2 \times \sqrt{ 49-2 } \left( 6+2 \sqrt{ 3 } +3 \sqrt{ 2 } - \sqrt{ 9 } - \sqrt{ 12 } - \sqrt{ 18 } \right)$$

Evalwa

$$6\sqrt{47}\approx 41.133927602$$

Passi tas-Soluzzjonijiet

Naqqas 2 minn 49 biex tikseb 47.

$$2\sqrt{47}\left(6+2\sqrt{3}+3\sqrt{2}-\sqrt{9}-\sqrt{12}-\sqrt{18}\right)$$

Ikkalkula l-għerq kwadrat ta' 9 u ikseb 3.

$$2\sqrt{47}\left(6+2\sqrt{3}+3\sqrt{2}-3-\sqrt{12}-\sqrt{18}\right)$$

Naqqas 3 minn 6 biex tikseb 3.

$$2\sqrt{47}\left(3+2\sqrt{3}+3\sqrt{2}-\sqrt{12}-\sqrt{18}\right)$$

Iffattura 12=2^{2}\times 3. Erġa' ikteb l-għerq kwadrat tal-prodott \sqrt{2^{2}\times 3} bħala l-prodott tal-għeruq kwadrati \sqrt{2^{2}}\sqrt{3}. Ħu l-għerq kwadrat ta' 2^{2}.

$$2\sqrt{47}\left(3+2\sqrt{3}+3\sqrt{2}-2\sqrt{3}-\sqrt{18}\right)$$

Ikkombina 2\sqrt{3} u -2\sqrt{3} biex tikseb 0.

$$2\sqrt{47}\left(3+3\sqrt{2}-\sqrt{18}\right)$$

Iffattura 18=3^{2}\times 2. Erġa' ikteb l-għerq kwadrat tal-prodott \sqrt{3^{2}\times 2} bħala l-prodott tal-għeruq kwadrati \sqrt{3^{2}}\sqrt{2}. Ħu l-għerq kwadrat ta' 3^{2}.

$$2\sqrt{47}\left(3+3\sqrt{2}-3\sqrt{2}\right)$$

Ikkombina 3\sqrt{2} u -3\sqrt{2} biex tikseb 0.

$$2\sqrt{47}\times 3$$

Immultiplika 2 u 3 biex tikseb 6.

$$6\sqrt{47}$$