Issolvi sqrt{frac{3/2}}{sqrt{1/8}}

$$\frac { \sqrt { \frac { 3 } { 2 } } } { \sqrt { \frac { 1 } { 8 } } }$$

Evalwa

$$2\sqrt{3}\approx 3.464101615$$

Passi tas-Soluzzjonijiet

Erġa' ikteb id-diviżjoni tal-għerq kwadrat \sqrt{\frac{3}{2}} bħala d-diviżjoni tal-għeruq kwadrati \frac{\sqrt{3}}{\sqrt{2}}.

$$\frac{\frac{\sqrt{3}}{\sqrt{2}}}{\sqrt{\frac{1}{8}}}$$

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

$$\frac{\frac{\sqrt{3}\sqrt{2}}{\left(\sqrt{2}\right)^{2}}}{\sqrt{\frac{1}{8}}}$$

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

$$\frac{\frac{\sqrt{3}\sqrt{2}}{2}}{\sqrt{\frac{1}{8}}}$$

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

$$\frac{\frac{\sqrt{6}}{2}}{\sqrt{\frac{1}{8}}}$$

Erġa' ikteb id-diviżjoni tal-għerq kwadrat \sqrt{\frac{1}{8}} bħala d-diviżjoni tal-għeruq kwadrati \frac{\sqrt{1}}{\sqrt{8}}.

$$\frac{\frac{\sqrt{6}}{2}}{\frac{\sqrt{1}}{\sqrt{8}}}$$

Ikkalkula l-għerq kwadrat ta' 1 u ikseb 1.

$$\frac{\frac{\sqrt{6}}{2}}{\frac{1}{\sqrt{8}}}$$

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}.

$$\frac{\frac{\sqrt{6}}{2}}{\frac{1}{2\sqrt{2}}}$$

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

$$\frac{\frac{\sqrt{6}}{2}}{\frac{\sqrt{2}}{2\left(\sqrt{2}\right)^{2}}}$$

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

$$\frac{\frac{\sqrt{6}}{2}}{\frac{\sqrt{2}}{2\times 2}}$$

Immultiplika 2 u 2 biex tikseb 4.

$$\frac{\frac{\sqrt{6}}{2}}{\frac{\sqrt{2}}{4}}$$

Iddividi \frac{\sqrt{6}}{2} b'\frac{\sqrt{2}}{4} billi timmultiplika \frac{\sqrt{6}}{2} bir-reċiproku ta' \frac{\sqrt{2}}{4}.

$$\frac{\sqrt{6}\times 4}{2\sqrt{2}}$$

Annulla 2 fin-numeratur u d-denominatur.

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

Irrazzjonalizza d-denominatur tal-\frac{2\sqrt{6}}{\sqrt{2}} billi timmultiplika in-numeratur u d-denominatur mill-\sqrt{2}.

$$\frac{2\sqrt{6}\sqrt{2}}{\left(\sqrt{2}\right)^{2}}$$

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

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

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

$$\frac{2\sqrt{2}\sqrt{3}\sqrt{2}}{2}$$

Immultiplika \sqrt{2} u \sqrt{2} biex tikseb 2.

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

Annulla 2 u 2.

$$2\sqrt{3}$$