Issolvi (sqrt{8}-2sqrt{0.25)}-(sqrt{11/8}+sqrt{50}+2/3sqrt{12})

$$( \sqrt { 8 } - 2 \sqrt { 0.25 ) } - ( \sqrt { 1 \frac { 1 } { 8 } } + \sqrt { 50 } + \frac { 2 } { 3 } \sqrt { 12 } )$$

Evalwa

$$-\frac{4\sqrt{3}}{3}-\frac{15\sqrt{2}}{4}-1\approx -8.612701936$$

Passi tas-Soluzzjonijiet

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

$$2\sqrt{2}-2\sqrt{0.25}-\left(\sqrt{\frac{1\times 8+1}{8}}+\sqrt{50}+\frac{2}{3}\sqrt{12}\right)$$

Ikkalkula l-għerq kwadrat ta' 0.25 u ikseb 0.5.

$$2\sqrt{2}-2\times 0.5-\left(\sqrt{\frac{1\times 8+1}{8}}+\sqrt{50}+\frac{2}{3}\sqrt{12}\right)$$

Immultiplika -2 u 0.5 biex tikseb -1.

$$2\sqrt{2}-1-\left(\sqrt{\frac{1\times 8+1}{8}}+\sqrt{50}+\frac{2}{3}\sqrt{12}\right)$$

Immultiplika 1 u 8 biex tikseb 8.

$$2\sqrt{2}-1-\left(\sqrt{\frac{8+1}{8}}+\sqrt{50}+\frac{2}{3}\sqrt{12}\right)$$

Żid 8 u 1 biex tikseb 9.

$$2\sqrt{2}-1-\left(\sqrt{\frac{9}{8}}+\sqrt{50}+\frac{2}{3}\sqrt{12}\right)$$

Erġa' ikteb id-diviżjoni tal-għerq kwadrat \sqrt{\frac{9}{8}} bħala d-diviżjoni tal-għeruq kwadrati \frac{\sqrt{9}}{\sqrt{8}}.

$$2\sqrt{2}-1-\left(\frac{\sqrt{9}}{\sqrt{8}}+\sqrt{50}+\frac{2}{3}\sqrt{12}\right)$$

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

$$2\sqrt{2}-1-\left(\frac{3}{\sqrt{8}}+\sqrt{50}+\frac{2}{3}\sqrt{12}\right)$$

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

$$2\sqrt{2}-1-\left(\frac{3}{2\sqrt{2}}+\sqrt{50}+\frac{2}{3}\sqrt{12}\right)$$

Irrazzjonalizza d-denominatur tal-\frac{3}{2\sqrt{2}} billi timmultiplika in-numeratur u d-denominatur mill-\sqrt{2}.

$$2\sqrt{2}-1-\left(\frac{3\sqrt{2}}{2\left(\sqrt{2}\right)^{2}}+\sqrt{50}+\frac{2}{3}\sqrt{12}\right)$$

Il-kwadrat ta' \sqrt{2} huwa 2.

$$2\sqrt{2}-1-\left(\frac{3\sqrt{2}}{2\times 2}+\sqrt{50}+\frac{2}{3}\sqrt{12}\right)$$

Immultiplika 2 u 2 biex tikseb 4.

$$2\sqrt{2}-1-\left(\frac{3\sqrt{2}}{4}+\sqrt{50}+\frac{2}{3}\sqrt{12}\right)$$

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}.

$$2\sqrt{2}-1-\left(\frac{3\sqrt{2}}{4}+5\sqrt{2}+\frac{2}{3}\sqrt{12}\right)$$

Ikkombina \frac{3\sqrt{2}}{4} u 5\sqrt{2} biex tikseb \frac{23}{4}\sqrt{2}.

$$2\sqrt{2}-1-\left(\frac{23}{4}\sqrt{2}+\frac{2}{3}\sqrt{12}\right)$$

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}.

$$2\sqrt{2}-1-\left(\frac{23}{4}\sqrt{2}+\frac{2}{3}\times 2\sqrt{3}\right)$$

Esprimi \frac{2}{3}\times 2 bħala frazzjoni waħda.

$$2\sqrt{2}-1-\left(\frac{23}{4}\sqrt{2}+\frac{2\times 2}{3}\sqrt{3}\right)$$

Immultiplika 2 u 2 biex tikseb 4.

$$2\sqrt{2}-1-\left(\frac{23}{4}\sqrt{2}+\frac{4}{3}\sqrt{3}\right)$$

Biex issib l-oppost ta' \frac{23}{4}\sqrt{2}+\frac{4}{3}\sqrt{3}, sib l-oppost ta' kull terminu.

$$2\sqrt{2}-1-\frac{23}{4}\sqrt{2}-\frac{4}{3}\sqrt{3}$$

Ikkombina 2\sqrt{2} u -\frac{23}{4}\sqrt{2} biex tikseb -\frac{15}{4}\sqrt{2}.

$$-\frac{15}{4}\sqrt{2}-1-\frac{4}{3}\sqrt{3}$$

Fattur

$$\frac{-16 \sqrt{3} - 45 \sqrt{2} - 12}{12} = -8.61270193565761$$