Datrys sqrt{45}+3sqrt{20}+sqrt{80}+4sqrt{40}

$$\sqrt { 45 } + 3 \sqrt { 20 } + \sqrt { 80 } + 4 \sqrt { 40 }$$

Enrhifo

$$8\sqrt{10}+13\sqrt{5}\approx 54.367104989$$

Camau Ateb

Ffactora 45=3^{2}\times 5. Ailysgrifennu ail isradd y lluoswm \sqrt{3^{2}\times 5} fel lluoswm ail israddau \sqrt{3^{2}}\sqrt{5}. Cymryd isradd 3^{2}.

$$3\sqrt{5}+3\sqrt{20}+\sqrt{80}+4\sqrt{40}$$

Ffactora 20=2^{2}\times 5. Ailysgrifennu ail isradd y lluoswm \sqrt{2^{2}\times 5} fel lluoswm ail israddau \sqrt{2^{2}}\sqrt{5}. Cymryd isradd 2^{2}.

$$3\sqrt{5}+3\times 2\sqrt{5}+\sqrt{80}+4\sqrt{40}$$

Lluosi 3 a 2 i gael 6.

$$3\sqrt{5}+6\sqrt{5}+\sqrt{80}+4\sqrt{40}$$

Cyfuno 3\sqrt{5} a 6\sqrt{5} i gael 9\sqrt{5}.

$$9\sqrt{5}+\sqrt{80}+4\sqrt{40}$$

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}.

$$9\sqrt{5}+4\sqrt{5}+4\sqrt{40}$$

Cyfuno 9\sqrt{5} a 4\sqrt{5} i gael 13\sqrt{5}.

$$13\sqrt{5}+4\sqrt{40}$$

Ffactora 40=2^{2}\times 10. Ailysgrifennu ail isradd y lluoswm \sqrt{2^{2}\times 10} fel lluoswm ail israddau \sqrt{2^{2}}\sqrt{10}. Cymryd isradd 2^{2}.

$$13\sqrt{5}+4\times 2\sqrt{10}$$

Lluosi 4 a 2 i gael 8.

$$13\sqrt{5}+8\sqrt{10}$$