Datrys sqrt{80}-2sqrt{252}+3sqrt{405}-3sqrt{500}

$$\sqrt { 80 } - 2 \sqrt { 252 } + 3 \sqrt { 405 } - 3 \sqrt { 500 }$$

Enrhifo

$$\sqrt{5}-12\sqrt{7}\approx -29.512947755$$

Camau Ateb

Ffactora 80=4^{2}\times 5. Ailysgrifennu ail isradd y lluoswm \sqrt{4^{2}\times 5} fel lluoswm ail israddau \sqrt{4^{2}}\sqrt{5}. Cymryd isradd 4^{2}.

$$4\sqrt{5}-2\sqrt{252}+3\sqrt{405}-3\sqrt{500}$$

Ffactora 252=6^{2}\times 7. Ailysgrifennu ail isradd y lluoswm \sqrt{6^{2}\times 7} fel lluoswm ail israddau \sqrt{6^{2}}\sqrt{7}. Cymryd isradd 6^{2}.

$$4\sqrt{5}-2\times 6\sqrt{7}+3\sqrt{405}-3\sqrt{500}$$

Lluosi -2 a 6 i gael -12.

$$4\sqrt{5}-12\sqrt{7}+3\sqrt{405}-3\sqrt{500}$$

Ffactora 405=9^{2}\times 5. Ailysgrifennu ail isradd y lluoswm \sqrt{9^{2}\times 5} fel lluoswm ail israddau \sqrt{9^{2}}\sqrt{5}. Cymryd isradd 9^{2}.

$$4\sqrt{5}-12\sqrt{7}+3\times 9\sqrt{5}-3\sqrt{500}$$

Lluosi 3 a 9 i gael 27.

$$4\sqrt{5}-12\sqrt{7}+27\sqrt{5}-3\sqrt{500}$$

Cyfuno 4\sqrt{5} a 27\sqrt{5} i gael 31\sqrt{5}.

$$31\sqrt{5}-12\sqrt{7}-3\sqrt{500}$$

Ffactora 500=10^{2}\times 5. Ailysgrifennu ail isradd y lluoswm \sqrt{10^{2}\times 5} fel lluoswm ail israddau \sqrt{10^{2}}\sqrt{5}. Cymryd isradd 10^{2}.

$$31\sqrt{5}-12\sqrt{7}-3\times 10\sqrt{5}$$

Lluosi -3 a 10 i gael -30.

$$31\sqrt{5}-12\sqrt{7}-30\sqrt{5}$$

Cyfuno 31\sqrt{5} a -30\sqrt{5} i gael \sqrt{5}.

$$\sqrt{5}-12\sqrt{7}$$