Issolvi sqrt{15}divsqrt{12}*sqrt{3/2}

$$\sqrt { 15 } \div \sqrt { 12 } \times \sqrt { \frac { 3 } { 2 } }$$

Evalwa

$$\frac{\sqrt{30}}{4}\approx 1.369306394$$

Passi tas-Soluzzjonijiet

Iffattura 12=2^{2}\times 3. Erġa' ikteb l-għerq kwadrat tal-prodott \sqrt{2^{2}\times 3} bħala l-prodott tal-għeruq kwadrati \sqrt{2^{2}}\sqrt{3}. Ħu l-għerq kwadrat ta' 2^{2}.

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

Irrazzjonalizza d-denominatur tal-\frac{\sqrt{15}}{2\sqrt{3}} billi timmultiplika in-numeratur u d-denominatur mill-\sqrt{3}.

$$\frac{\sqrt{15}\sqrt{3}}{2\left(\sqrt{3}\right)^{2}}\sqrt{\frac{3}{2}}$$

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

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

Iffattura 15=3\times 5. Erġa' ikteb l-għerq kwadrat tal-prodott \sqrt{3\times 5} bħala l-prodott tal-għeruq kwadrati \sqrt{3}\sqrt{5}.

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

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

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

Immultiplika 2 u 3 biex tikseb 6.

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

Iddividi 3\sqrt{5} b'6 biex tikseb\frac{1}{2}\sqrt{5}.

$$\frac{1}{2}\sqrt{5}\sqrt{\frac{3}{2}}$$

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

$$\frac{1}{2}\sqrt{5}\times \frac{\sqrt{3}}{\sqrt{2}}$$

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

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

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

$$\frac{1}{2}\sqrt{5}\times \frac{\sqrt{3}\sqrt{2}}{2}$$

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

$$\frac{1}{2}\sqrt{5}\times \frac{\sqrt{6}}{2}$$

Immultiplika \frac{1}{2} b'\frac{\sqrt{6}}{2} billi timmultiplika n-numeratur bin-numeratur u d-denominatur bid-denominatur.

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

Immultiplika 2 u 2 biex tikseb 4.

$$\frac{\sqrt{6}}{4}\sqrt{5}$$

Esprimi \frac{\sqrt{6}}{4}\sqrt{5} bħala frazzjoni waħda.

$$\frac{\sqrt{6}\sqrt{5}}{4}$$

Biex timmultiplika \sqrt{6} u \sqrt{5}, immultiplika n-numri taħt l-għerq kwadrat.

$$\frac{\sqrt{30}}{4}$$