Datrys sqrt{75}+3sqrt{18}-2sqrt{12}-2sqrt{50}

$$\sqrt { 75 } + 3 \sqrt { 18 } - 2 \sqrt { 12 } - 2 \sqrt { 50 }$$

Enrhifo

$$\sqrt{3}-\sqrt{2}\approx 0.317837245$$

Camau Ateb

Ffactora 75=5^{2}\times 3. Ailysgrifennu ail isradd y lluoswm \sqrt{5^{2}\times 3} fel lluoswm ail israddau \sqrt{5^{2}}\sqrt{3}. Cymryd isradd 5^{2}.

$$5\sqrt{3}+3\sqrt{18}-2\sqrt{12}-2\sqrt{50}$$

Ffactora 18=3^{2}\times 2. Ailysgrifennu ail isradd y lluoswm \sqrt{3^{2}\times 2} fel lluoswm ail israddau \sqrt{3^{2}}\sqrt{2}. Cymryd isradd 3^{2}.

$$5\sqrt{3}+3\times 3\sqrt{2}-2\sqrt{12}-2\sqrt{50}$$

Lluosi 3 a 3 i gael 9.

$$5\sqrt{3}+9\sqrt{2}-2\sqrt{12}-2\sqrt{50}$$

Ffactora 12=2^{2}\times 3. Ailysgrifennu ail isradd y lluoswm \sqrt{2^{2}\times 3} fel lluoswm ail israddau \sqrt{2^{2}}\sqrt{3}. Cymryd isradd 2^{2}.

$$5\sqrt{3}+9\sqrt{2}-2\times 2\sqrt{3}-2\sqrt{50}$$

Lluosi -2 a 2 i gael -4.

$$5\sqrt{3}+9\sqrt{2}-4\sqrt{3}-2\sqrt{50}$$

Cyfuno 5\sqrt{3} a -4\sqrt{3} i gael \sqrt{3}.

$$\sqrt{3}+9\sqrt{2}-2\sqrt{50}$$

Ffactora 50=5^{2}\times 2. Ailysgrifennu ail isradd y lluoswm \sqrt{5^{2}\times 2} fel lluoswm ail israddau \sqrt{5^{2}}\sqrt{2}. Cymryd isradd 5^{2}.

$$\sqrt{3}+9\sqrt{2}-2\times 5\sqrt{2}$$

Lluosi -2 a 5 i gael -10.

$$\sqrt{3}+9\sqrt{2}-10\sqrt{2}$$

Cyfuno 9\sqrt{2} a -10\sqrt{2} i gael -\sqrt{2}.

$$\sqrt{3}-\sqrt{2}$$