Datrys sqrt{80}+5sqrt{1/2}-3sqrt{5}+1/5sqrt{125}

$$\sqrt{ 80 } +5 \sqrt{ \frac{ 1 }{ 2 } } -3 \sqrt{ 5 } + \frac{ 1 }{ 5 } \sqrt{ 125 }$$

Enrhifo

$$\frac{\sqrt{5}\left(\sqrt{10}+4\right)}{2}\approx 8.007669861$$

Camau Ateb Byr

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}.

$$4\sqrt{5}+5\sqrt{\frac{1}{2}}-3\sqrt{5}+\frac{1}{5}\sqrt{125}$$

Ailysgrifennu ail isradd y rhaniad \sqrt{\frac{1}{2}} fel rhaniad ail israddau \frac{\sqrt{1}}{\sqrt{2}}.

$$4\sqrt{5}+5\times \frac{\sqrt{1}}{\sqrt{2}}-3\sqrt{5}+\frac{1}{5}\sqrt{125}$$

Cyfrifo ail isradd 1 a chael 1.

$$4\sqrt{5}+5\times \frac{1}{\sqrt{2}}-3\sqrt{5}+\frac{1}{5}\sqrt{125}$$

Mae'n rhesymoli enwadur \frac{1}{\sqrt{2}} drwy luosi'r rhifiadur a'r enwadur â \sqrt{2}.

$$4\sqrt{5}+5\times \frac{\sqrt{2}}{\left(\sqrt{2}\right)^{2}}-3\sqrt{5}+\frac{1}{5}\sqrt{125}$$

Sgwâr \sqrt{2} yw 2.

$$4\sqrt{5}+5\times \frac{\sqrt{2}}{2}-3\sqrt{5}+\frac{1}{5}\sqrt{125}$$

Mynegwch 5\times \frac{\sqrt{2}}{2} fel ffracsiwn unigol.

$$4\sqrt{5}+\frac{5\sqrt{2}}{2}-3\sqrt{5}+\frac{1}{5}\sqrt{125}$$

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

$$\sqrt{5}+\frac{5\sqrt{2}}{2}+\frac{1}{5}\sqrt{125}$$

Ffactora 125=5^{2}\times 5. Ailysgrifennu ail isradd y lluoswm \sqrt{5^{2}\times 5} fel lluoswm ail israddau \sqrt{5^{2}}\sqrt{5}. Cymryd isradd 5^{2}.

$$\sqrt{5}+\frac{5\sqrt{2}}{2}+\frac{1}{5}\times 5\sqrt{5}$$

Canslo 5 a 5.

$$\sqrt{5}+\frac{5\sqrt{2}}{2}+\sqrt{5}$$

Cyfuno \sqrt{5} a \sqrt{5} i gael 2\sqrt{5}.

$$2\sqrt{5}+\frac{5\sqrt{2}}{2}$$

I ychwanegu neu dynnu mynegiannau, rhaid i chi eu ehangu i wneud eu enwaduron yr un fath. Lluoswch 2\sqrt{5} â \frac{2}{2}.

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

Gan fod gan \frac{2\times 2\sqrt{5}}{2} a \frac{5\sqrt{2}}{2} yr un dynodydd, adiwch nhw drwy adio eu rhifiaduron.

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

Gwnewch y gwaith lluosi yn 2\times 2\sqrt{5}+5\sqrt{2}.

$$\frac{4\sqrt{5}+5\sqrt{2}}{2}$$

Ffactor

$$\frac{\sqrt{5} {(\sqrt{2} \sqrt{5} + 4)}}{2} = 8.007669860932317$$