Issolvi -sqrt{27}div(3/10)sqrt{3/8}

$$- \sqrt { 27 } \div ( \frac { 3 } { 10 } ) \sqrt { \frac { 3 } { 8 } }$$

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}.

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

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

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

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}.

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

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

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

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

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

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

$$\frac{-3\sqrt{3}}{\frac{3}{10}}\times \frac{\sqrt{6}}{2\times 2}$$

Immultiplika 2 u 2 biex tikseb 4.

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

Iddividi -3\sqrt{3} b'\frac{3}{10} billi timmultiplika -3\sqrt{3} bir-reċiproku ta' \frac{3}{10}.

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

Immultiplika \frac{\left(-3\sqrt{3}\right)\times 10}{3} b'\frac{\sqrt{6}}{4} billi timmultiplika n-numeratur bin-numeratur u d-denominatur bid-denominatur.

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

Annulla 2 fin-numeratur u d-denominatur.

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

Immultiplika 5 u -1 biex tikseb -5.

$$\frac{-5\times 3\sqrt{3}\sqrt{6}}{2\times 3}$$

Immultiplika -5 u 3 biex tikseb -15.

$$\frac{-15\sqrt{3}\sqrt{6}}{2\times 3}$$

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}.

$$\frac{-15\sqrt{3}\sqrt{3}\sqrt{2}}{2\times 3}$$

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

$$\frac{-15\times 3\sqrt{2}}{2\times 3}$$

Immultiplika 2 u 3 biex tikseb 6.

$$\frac{-15\times 3\sqrt{2}}{6}$$

Immultiplika -15 u 3 biex tikseb -45.

$$\frac{-45\sqrt{2}}{6}$$

Iddividi -45\sqrt{2} b'6 biex tikseb-\frac{15}{2}\sqrt{2}.

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