Issolvi -{[(1/sqrt{2})-(-1/sqrt{5})]+(-sqrt{4})^3+2(sqrt{16}-1/2)}div(3/4)

$$- \{ [ ( \frac { 1 } { \sqrt { 2 } } ) - ( - \frac { 1 } { \sqrt { 5 } } ) ] + ( - \sqrt { 4 } ) ^ { 3 } + 2 ( \sqrt { 16 } - \frac { 1 } { 2 } ) \} \div ( \frac { 3 } { 4 } )$$

Evalwa

$$-\frac{2\sqrt{2}}{3}-\frac{4\sqrt{5}}{15}+\frac{4}{3}\approx -0.205760502$$

Passi Qosra tas-Soluzzjonijiet

Irrazzjonalizza d-denominatur tal-\frac{1}{\sqrt{2}} billi timmultiplika in-numeratur u d-denominatur mill-\sqrt{2}.

$$\frac{-\left(\frac{\sqrt{2}}{\left(\sqrt{2}\right)^{2}}-\left(-\frac{1}{\sqrt{5}}\right)+\left(-\sqrt{4}\right)^{3}+2\left(\sqrt{16}-\frac{1}{2}\right)\right)}{\frac{3}{4}}$$

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

$$\frac{-\left(\frac{\sqrt{2}}{2}-\left(-\frac{1}{\sqrt{5}}\right)+\left(-\sqrt{4}\right)^{3}+2\left(\sqrt{16}-\frac{1}{2}\right)\right)}{\frac{3}{4}}$$

Irrazzjonalizza d-denominatur tal-\frac{1}{\sqrt{5}} billi timmultiplika in-numeratur u d-denominatur mill-\sqrt{5}.

$$\frac{-\left(\frac{\sqrt{2}}{2}-\left(-\frac{\sqrt{5}}{\left(\sqrt{5}\right)^{2}}\right)+\left(-\sqrt{4}\right)^{3}+2\left(\sqrt{16}-\frac{1}{2}\right)\right)}{\frac{3}{4}}$$

Il-kwadrat ta' \sqrt{5} huwa 5.

$$\frac{-\left(\frac{\sqrt{2}}{2}-\left(-\frac{\sqrt{5}}{5}\right)+\left(-\sqrt{4}\right)^{3}+2\left(\sqrt{16}-\frac{1}{2}\right)\right)}{\frac{3}{4}}$$

Ikkalkula l-għerq kwadrat ta' 4 u ikseb 2.

$$\frac{-\left(\frac{\sqrt{2}}{2}-\left(-\frac{\sqrt{5}}{5}\right)+\left(-2\right)^{3}+2\left(\sqrt{16}-\frac{1}{2}\right)\right)}{\frac{3}{4}}$$

Ikkalkula -2 bil-power ta' 3 u tikseb -8.

$$\frac{-\left(\frac{\sqrt{2}}{2}-\left(-\frac{\sqrt{5}}{5}\right)-8+2\left(\sqrt{16}-\frac{1}{2}\right)\right)}{\frac{3}{4}}$$

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

$$\frac{-\left(\frac{\sqrt{2}}{2}-\left(-\frac{\sqrt{5}}{5}\right)-8+2\left(4-\frac{1}{2}\right)\right)}{\frac{3}{4}}$$

Naqqas \frac{1}{2} minn 4 biex tikseb \frac{7}{2}.

$$\frac{-\left(\frac{\sqrt{2}}{2}-\left(-\frac{\sqrt{5}}{5}\right)-8+2\times \frac{7}{2}\right)}{\frac{3}{4}}$$

Immultiplika 2 u \frac{7}{2} biex tikseb 7.

$$\frac{-\left(\frac{\sqrt{2}}{2}-\left(-\frac{\sqrt{5}}{5}\right)-8+7\right)}{\frac{3}{4}}$$

Żid -8 u 7 biex tikseb -1.

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

Biex issib l-oppost ta' \frac{\sqrt{2}}{2}-\left(-\frac{\sqrt{5}}{5}\right)-1, sib l-oppost ta' kull terminu.

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

Iddividi -\left(\frac{\sqrt{2}}{2}-\left(-\frac{\sqrt{5}}{5}\right)\right)+1 b'\frac{3}{4} billi timmultiplika -\left(\frac{\sqrt{2}}{2}-\left(-\frac{\sqrt{5}}{5}\right)\right)+1 bir-reċiproku ta' \frac{3}{4}.

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

Immultiplika -1 u -1 biex tikseb 1.

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

Biex iżżid jew tnaqqas l-espressjonijiet, espandihom biex id-denominaturi tagħhom ikunu l-istess. L-inqas multiplu komuni ta' 2 u 5 huwa 10. Immultiplika \frac{\sqrt{2}}{2} b'\frac{5}{5}. Immultiplika \frac{\sqrt{5}}{5} b'\frac{2}{2}.

$$\frac{\left(-\left(\frac{5\sqrt{2}}{10}+\frac{2\sqrt{5}}{10}\right)+1\right)\times 4}{3}$$

Billi \frac{5\sqrt{2}}{10} u \frac{2\sqrt{5}}{10} għandhom l-istess denominatur, żidhom billi żżid in-numeraturi tagħhom.

$$\frac{\left(-\frac{5\sqrt{2}+2\sqrt{5}}{10}+1\right)\times 4}{3}$$

Biex iżżid jew tnaqqas l-espressjonijiet, espandihom biex id-denominaturi tagħhom ikunu l-istess. Immultiplika 1 b'\frac{10}{10}.

$$\frac{\left(-\frac{5\sqrt{2}+2\sqrt{5}}{10}+\frac{10}{10}\right)\times 4}{3}$$

Billi -\frac{5\sqrt{2}+2\sqrt{5}}{10} u \frac{10}{10} għandhom l-istess denominatur, żidhom billi żżid in-numeraturi tagħhom.

$$\frac{\frac{-\left(5\sqrt{2}+2\sqrt{5}\right)+10}{10}\times 4}{3}$$

Agħmel il-multiplikazzjonijiet fi -\left(5\sqrt{2}+2\sqrt{5}\right)+10.

$$\frac{\frac{-5\sqrt{2}-2\sqrt{5}+10}{10}\times 4}{3}$$

Esprimi \frac{-5\sqrt{2}-2\sqrt{5}+10}{10}\times 4 bħala frazzjoni waħda.

$$\frac{\frac{\left(-5\sqrt{2}-2\sqrt{5}+10\right)\times 4}{10}}{3}$$

Esprimi \frac{\frac{\left(-5\sqrt{2}-2\sqrt{5}+10\right)\times 4}{10}}{3} bħala frazzjoni waħda.

$$\frac{\left(-5\sqrt{2}-2\sqrt{5}+10\right)\times 4}{10\times 3}$$

Annulla 2 fin-numeratur u d-denominatur.

$$\frac{2\left(-5\sqrt{2}-2\sqrt{5}+10\right)}{3\times 5}$$

Immultiplika 3 u 5 biex tikseb 15.

$$\frac{2\left(-5\sqrt{2}-2\sqrt{5}+10\right)}{15}$$

Uża l-propjetà distributtiva biex timmultiplika 2 b'-5\sqrt{2}-2\sqrt{5}+10.

$$\frac{-10\sqrt{2}-4\sqrt{5}+20}{15}$$