Issolvi 3sqrt{22/3}+1/2sqrt{2/5}*(-1/8sqrt{15})

$$3 \sqrt { 2 \frac { 2 } { 3 } } + \frac { 1 } { 2 } \sqrt { \frac { 2 } { 5 } } \times ( - \frac { 1 } { 8 } \sqrt { 15 } )$$

Evalwa

$$\frac{31\sqrt{6}}{16}\approx 4.745886377$$

Passi Qosra tas-Soluzzjonijiet

Immultiplika 2 u 3 biex tikseb 6.

$$3\sqrt{\frac{6+2}{3}}+\frac{1}{2}\sqrt{\frac{2}{5}}\left(-\frac{1}{8}\right)\sqrt{15}$$

Żid 6 u 2 biex tikseb 8.

$$3\sqrt{\frac{8}{3}}+\frac{1}{2}\sqrt{\frac{2}{5}}\left(-\frac{1}{8}\right)\sqrt{15}$$

Erġa' ikteb id-diviżjoni tal-għerq kwadrat \sqrt{\frac{8}{3}} bħala d-diviżjoni tal-għeruq kwadrati \frac{\sqrt{8}}{\sqrt{3}}.

$$3\times \frac{\sqrt{8}}{\sqrt{3}}+\frac{1}{2}\sqrt{\frac{2}{5}}\left(-\frac{1}{8}\right)\sqrt{15}$$

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}.

$$3\times \frac{2\sqrt{2}}{\sqrt{3}}+\frac{1}{2}\sqrt{\frac{2}{5}}\left(-\frac{1}{8}\right)\sqrt{15}$$

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

$$3\times \frac{2\sqrt{2}\sqrt{3}}{\left(\sqrt{3}\right)^{2}}+\frac{1}{2}\sqrt{\frac{2}{5}}\left(-\frac{1}{8}\right)\sqrt{15}$$

Il-kwadrat ta' \sqrt{3} huwa 3.

$$3\times \frac{2\sqrt{2}\sqrt{3}}{3}+\frac{1}{2}\sqrt{\frac{2}{5}}\left(-\frac{1}{8}\right)\sqrt{15}$$

Biex timmultiplika \sqrt{2} u \sqrt{3}, immultiplika n-numri taħt l-għerq kwadrat.

$$3\times \frac{2\sqrt{6}}{3}+\frac{1}{2}\sqrt{\frac{2}{5}}\left(-\frac{1}{8}\right)\sqrt{15}$$

Annulla 3 u 3.

$$2\sqrt{6}+\frac{1}{2}\sqrt{\frac{2}{5}}\left(-\frac{1}{8}\right)\sqrt{15}$$

Erġa' ikteb id-diviżjoni tal-għerq kwadrat \sqrt{\frac{2}{5}} bħala d-diviżjoni tal-għeruq kwadrati \frac{\sqrt{2}}{\sqrt{5}}.

$$2\sqrt{6}+\frac{1}{2}\times \frac{\sqrt{2}}{\sqrt{5}}\left(-\frac{1}{8}\right)\sqrt{15}$$

Irrazzjonalizza d-denominatur tal-\frac{\sqrt{2}}{\sqrt{5}} billi timmultiplika in-numeratur u d-denominatur mill-\sqrt{5}.

$$2\sqrt{6}+\frac{1}{2}\times \frac{\sqrt{2}\sqrt{5}}{\left(\sqrt{5}\right)^{2}}\left(-\frac{1}{8}\right)\sqrt{15}$$

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

$$2\sqrt{6}+\frac{1}{2}\times \frac{\sqrt{2}\sqrt{5}}{5}\left(-\frac{1}{8}\right)\sqrt{15}$$

Biex timmultiplika \sqrt{2} u \sqrt{5}, immultiplika n-numri taħt l-għerq kwadrat.

$$2\sqrt{6}+\frac{1}{2}\times \frac{\sqrt{10}}{5}\left(-\frac{1}{8}\right)\sqrt{15}$$

Immultiplika \frac{1}{2} b'-\frac{1}{8} billi timmultiplika n-numeratur bin-numeratur u d-denominatur bid-denominatur.

$$2\sqrt{6}+\frac{1\left(-1\right)}{2\times 8}\times \frac{\sqrt{10}}{5}\sqrt{15}$$

Agħmel il-multiplikazzjonijiet fil-frazzjoni \frac{1\left(-1\right)}{2\times 8}.

$$2\sqrt{6}+\frac{-1}{16}\times \frac{\sqrt{10}}{5}\sqrt{15}$$

Frazzjoni \frac{-1}{16} tista' tinkiteb mill-ġdid bħala -\frac{1}{16} bl-estrazzjoni tas-sinjal negattiv.

$$2\sqrt{6}-\frac{1}{16}\times \frac{\sqrt{10}}{5}\sqrt{15}$$

Immultiplika -\frac{1}{16} b'\frac{\sqrt{10}}{5} billi timmultiplika n-numeratur bin-numeratur u d-denominatur bid-denominatur.

$$2\sqrt{6}+\frac{-\sqrt{10}}{16\times 5}\sqrt{15}$$

Esprimi \frac{-\sqrt{10}}{16\times 5}\sqrt{15} bħala frazzjoni waħda.

$$2\sqrt{6}+\frac{-\sqrt{10}\sqrt{15}}{16\times 5}$$

Biex iżżid jew tnaqqas l-espressjonijiet, espandihom biex id-denominaturi tagħhom ikunu l-istess. Immultiplika 2\sqrt{6} b'\frac{16\times 5}{16\times 5}.

$$\frac{2\sqrt{6}\times 16\times 5}{16\times 5}+\frac{-\sqrt{10}\sqrt{15}}{16\times 5}$$

Billi \frac{2\sqrt{6}\times 16\times 5}{16\times 5} u \frac{-\sqrt{10}\sqrt{15}}{16\times 5} għandhom l-istess denominatur, żidhom billi żżid in-numeraturi tagħhom.

$$\frac{2\sqrt{6}\times 16\times 5-\sqrt{10}\sqrt{15}}{16\times 5}$$

Agħmel il-multiplikazzjonijiet fi 2\sqrt{6}\times 16\times 5-\sqrt{10}\sqrt{15}.

$$\frac{160\sqrt{6}-5\sqrt{6}}{16\times 5}$$

Agħmel il-kalkoli fi 160\sqrt{6}-5\sqrt{6}.

$$\frac{155\sqrt{6}}{16\times 5}$$

Annulla 5 fin-numeratur u d-denominatur.

$$\frac{31\sqrt{6}}{16}$$