Issolvi sqrt{2}-sqrt{40}+3sqrt{50}-9sqrt{90}

$$\sqrt { 2 } - \sqrt { 40 } + 3 \sqrt { 50 } - 9 \sqrt { 90 }$$

Evalwa

$$16\sqrt{2}-29\sqrt{10}\approx -69.078635147$$

Passi tas-Soluzzjonijiet

Iffattura 40=2^{2}\times 10. Erġa' ikteb l-għerq kwadrat tal-prodott \sqrt{2^{2}\times 10} bħala l-prodott tal-għeruq kwadrati \sqrt{2^{2}}\sqrt{10}. Ħu l-għerq kwadrat ta' 2^{2}.

$$\sqrt{2}-2\sqrt{10}+3\sqrt{50}-9\sqrt{90}$$

Iffattura 50=5^{2}\times 2. Erġa' ikteb l-għerq kwadrat tal-prodott \sqrt{5^{2}\times 2} bħala l-prodott tal-għeruq kwadrati \sqrt{5^{2}}\sqrt{2}. Ħu l-għerq kwadrat ta' 5^{2}.

$$\sqrt{2}-2\sqrt{10}+3\times 5\sqrt{2}-9\sqrt{90}$$

Immultiplika 3 u 5 biex tikseb 15.

$$\sqrt{2}-2\sqrt{10}+15\sqrt{2}-9\sqrt{90}$$

Ikkombina \sqrt{2} u 15\sqrt{2} biex tikseb 16\sqrt{2}.

$$16\sqrt{2}-2\sqrt{10}-9\sqrt{90}$$

Iffattura 90=3^{2}\times 10. Erġa' ikteb l-għerq kwadrat tal-prodott \sqrt{3^{2}\times 10} bħala l-prodott tal-għeruq kwadrati \sqrt{3^{2}}\sqrt{10}. Ħu l-għerq kwadrat ta' 3^{2}.

$$16\sqrt{2}-2\sqrt{10}-9\times 3\sqrt{10}$$

Immultiplika -9 u 3 biex tikseb -27.

$$16\sqrt{2}-2\sqrt{10}-27\sqrt{10}$$

Ikkombina -2\sqrt{10} u -27\sqrt{10} biex tikseb -29\sqrt{10}.

$$16\sqrt{2}-29\sqrt{10}$$