Issolvi sqrt{75}*frac{sqrt{6}}{3}div1/sqrt{2}

$$\sqrt { 75 } \times \frac { \sqrt { 6 } } { 3 } \div \frac { 1 } { \sqrt { 2 } }$$

Evalwa

$$10$$

Passi tas-Soluzzjonijiet

Iffattura 75=5^{2}\times 3. Erġa' ikteb l-għerq kwadrat tal-prodott \sqrt{5^{2}\times 3} bħala l-prodott tal-għeruq kwadrati \sqrt{5^{2}}\sqrt{3}. Ħu l-għerq kwadrat ta' 5^{2}.

$$\frac{5\sqrt{3}\times \frac{\sqrt{6}}{3}}{\frac{1}{\sqrt{2}}}$$

Esprimi 5\times \frac{\sqrt{6}}{3} bħala frazzjoni waħda.

$$\frac{\frac{5\sqrt{6}}{3}\sqrt{3}}{\frac{1}{\sqrt{2}}}$$

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

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

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

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

Esprimi \frac{5\sqrt{6}}{3}\sqrt{3} bħala frazzjoni waħda.

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

Iddividi \frac{5\sqrt{6}\sqrt{3}}{3} b'\frac{\sqrt{2}}{2} billi timmultiplika \frac{5\sqrt{6}\sqrt{3}}{3} bir-reċiproku ta' \frac{\sqrt{2}}{2}.

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

Irrazzjonalizza d-denominatur tal-\frac{5\sqrt{6}\sqrt{3}\times 2}{3\sqrt{2}} billi timmultiplika in-numeratur u d-denominatur mill-\sqrt{2}.

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

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

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

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}.

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

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

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

Immultiplika 5 u 3 biex tikseb 15.

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

Immultiplika 15 u 2 biex tikseb 30.

$$\frac{30\sqrt{2}\sqrt{2}}{3\times 2}$$

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

$$\frac{30\times 2}{3\times 2}$$

Immultiplika 30 u 2 biex tikseb 60.

$$\frac{60}{3\times 2}$$

Immultiplika 3 u 2 biex tikseb 6.

$$\frac{60}{6}$$

Iddividi 60 b'6 biex tikseb10.

$$10$$

Fattur

$$2\times 5$$