Issolvi 2sqrt{3}-1/2*sqrt{5}*sqrt{3}divsqrt{20}

$$2 \sqrt { 3 } - \frac { 1 } { 2 } \times \sqrt { 5 } \times \sqrt { 3 } \div \sqrt { 20 }$$

Evalwa

$$\frac{7\sqrt{3}}{4}\approx 3.031088913$$

Passi tas-Soluzzjonijiet

Biex timmultiplika \sqrt{5} u \sqrt{3}, immultiplika n-numri taħt l-għerq kwadrat.

$$2\sqrt{3}-\frac{\frac{1}{2}\sqrt{15}}{\sqrt{20}}$$

Iffattura 20=2^{2}\times 5. Erġa' ikteb l-għerq kwadrat tal-prodott \sqrt{2^{2}\times 5} bħala l-prodott tal-għeruq kwadrati \sqrt{2^{2}}\sqrt{5}. Ħu l-għerq kwadrat ta' 2^{2}.

$$2\sqrt{3}-\frac{\frac{1}{2}\sqrt{15}}{2\sqrt{5}}$$

Irrazzjonalizza d-denominatur tal-\frac{\frac{1}{2}\sqrt{15}}{2\sqrt{5}} billi timmultiplika in-numeratur u d-denominatur mill-\sqrt{5}.

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

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

$$2\sqrt{3}-\frac{\frac{1}{2}\sqrt{15}\sqrt{5}}{2\times 5}$$

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

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

Immultiplika \sqrt{5} u \sqrt{5} biex tikseb 5.

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

Immultiplika 2 u 5 biex tikseb 10.

$$2\sqrt{3}-\frac{\frac{1}{2}\times 5\sqrt{3}}{10}$$

Immultiplika \frac{1}{2} u 5 biex tikseb \frac{5}{2}.

$$2\sqrt{3}-\frac{\frac{5}{2}\sqrt{3}}{10}$$

Iddividi \frac{5}{2}\sqrt{3} b'10 biex tikseb\frac{1}{4}\sqrt{3}.

$$2\sqrt{3}-\frac{1}{4}\sqrt{3}$$

Ikkombina 2\sqrt{3} u -\frac{1}{4}\sqrt{3} biex tikseb \frac{7}{4}\sqrt{3}.

$$\frac{7}{4}\sqrt{3}$$