Issolvi -sqrt{27}*10/3*sqrt{3/8}

$$- \sqrt { 27 } \times \frac { 10 } { 3 } \times \sqrt { \frac { 3 } { 8 } }$$

Evalwa

$$-\frac{15\sqrt{2}}{2}\approx -10.606601718$$

Passi tas-Soluzzjonijiet

Iffattura 27=3^{2}\times 3. Erġa' ikteb l-għerq kwadrat tal-prodott \sqrt{3^{2}\times 3} bħala l-prodott tal-għeruq kwadrati \sqrt{3^{2}}\sqrt{3}. Ħu l-għerq kwadrat ta' 3^{2}.

$$\left(-3\sqrt{3}\right)\times \frac{10}{3}\sqrt{\frac{3}{8}}$$

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

$$\left(-3\sqrt{3}\right)\times \frac{10}{3}\times \frac{\sqrt{3}}{\sqrt{8}}$$

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}.

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

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

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

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

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

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

$$\left(-3\sqrt{3}\right)\times \frac{10}{3}\times \frac{\sqrt{6}}{2\times 2}$$

Immultiplika 2 u 2 biex tikseb 4.

$$\left(-3\sqrt{3}\right)\times \frac{10}{3}\times \frac{\sqrt{6}}{4}$$

Esprimi \left(-3\sqrt{3}\right)\times \frac{\sqrt{6}}{4} bħala frazzjoni waħda.

$$\frac{-3\sqrt{3}\sqrt{6}}{4}\times \frac{10}{3}$$

Iffattura 6=3\times 2. Erġa' ikteb l-għerq kwadrat tal-prodott \sqrt{3\times 2} bħala l-prodott tal-għeruq kwadrati \sqrt{3}\sqrt{2}.

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

Immultiplika \sqrt{3} u \sqrt{3} biex tikseb 3.

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

Immultiplika -3 u 3 biex tikseb -9.

$$\frac{-9\sqrt{2}}{4}\times \frac{10}{3}$$

Immultiplika \frac{-9\sqrt{2}}{4} b'\frac{10}{3} billi timmultiplika n-numeratur bin-numeratur u d-denominatur bid-denominatur.

$$\frac{-9\sqrt{2}\times 10}{4\times 3}$$

Annulla 2\times 3 fin-numeratur u d-denominatur.

$$\frac{-3\times 5\sqrt{2}}{2}$$

Immultiplika -3 u 5 biex tikseb -15.

$$\frac{-15\sqrt{2}}{2}$$