Datrys sqrt{0.1(-14*5%)^2+0.3(-2.5%)^2+0.4(2.5%)^2+0.2(5.5%)^2}

$$\sqrt { 0.1 ( - 14 \cdot 5 \% ) ^ { 2 } + 0.3 ( - 2.5 \% ) ^ { 2 } + 0.4 ( 2.5 \% ) ^ { 2 } + 0.2 ( 5.5 \% ) ^ { 2 } }$$

Enrhifo

$$\frac{\sqrt{200170}}{2000}\approx 0.22370181$$

Camau Ateb

Lleihau'r ffracsiwn \frac{5}{100} i'r graddau lleiaf posib drwy dynnu a chanslo allan 5.

$$\sqrt{0.1\left(-14\times \frac{1}{20}\right)^{2}+0.3\left(-\frac{2.5}{100}\right)^{2}+0.4\times \left(\frac{2.5}{100}\right)^{2}+0.2\times \left(\frac{5.5}{100}\right)^{2}}$$

Lluosi -14 a \frac{1}{20} i gael -\frac{7}{10}.

$$\sqrt{0.1\left(-\frac{7}{10}\right)^{2}+0.3\left(-\frac{2.5}{100}\right)^{2}+0.4\times \left(\frac{2.5}{100}\right)^{2}+0.2\times \left(\frac{5.5}{100}\right)^{2}}$$

Cyfrifo -\frac{7}{10} i bŵer 2 a chael \frac{49}{100}.

$$\sqrt{0.1\times \frac{49}{100}+0.3\left(-\frac{2.5}{100}\right)^{2}+0.4\times \left(\frac{2.5}{100}\right)^{2}+0.2\times \left(\frac{5.5}{100}\right)^{2}}$$

Lluosi 0.1 a \frac{49}{100} i gael \frac{49}{1000}.

$$\sqrt{\frac{49}{1000}+0.3\left(-\frac{2.5}{100}\right)^{2}+0.4\times \left(\frac{2.5}{100}\right)^{2}+0.2\times \left(\frac{5.5}{100}\right)^{2}}$$

Ehangu \frac{2.5}{100} drwy luosi'r rhifiadur a'r enwadur gyda 10.

$$\sqrt{\frac{49}{1000}+0.3\left(-\frac{25}{1000}\right)^{2}+0.4\times \left(\frac{2.5}{100}\right)^{2}+0.2\times \left(\frac{5.5}{100}\right)^{2}}$$

Lleihau'r ffracsiwn \frac{25}{1000} i'r graddau lleiaf posib drwy dynnu a chanslo allan 25.

$$\sqrt{\frac{49}{1000}+0.3\left(-\frac{1}{40}\right)^{2}+0.4\times \left(\frac{2.5}{100}\right)^{2}+0.2\times \left(\frac{5.5}{100}\right)^{2}}$$

Cyfrifo -\frac{1}{40} i bŵer 2 a chael \frac{1}{1600}.

$$\sqrt{\frac{49}{1000}+0.3\times \frac{1}{1600}+0.4\times \left(\frac{2.5}{100}\right)^{2}+0.2\times \left(\frac{5.5}{100}\right)^{2}}$$

Lluosi 0.3 a \frac{1}{1600} i gael \frac{3}{16000}.

$$\sqrt{\frac{49}{1000}+\frac{3}{16000}+0.4\times \left(\frac{2.5}{100}\right)^{2}+0.2\times \left(\frac{5.5}{100}\right)^{2}}$$

Adio \frac{49}{1000} a \frac{3}{16000} i gael \frac{787}{16000}.

$$\sqrt{\frac{787}{16000}+0.4\times \left(\frac{2.5}{100}\right)^{2}+0.2\times \left(\frac{5.5}{100}\right)^{2}}$$

Ehangu \frac{2.5}{100} drwy luosi'r rhifiadur a'r enwadur gyda 10.

$$\sqrt{\frac{787}{16000}+0.4\times \left(\frac{25}{1000}\right)^{2}+0.2\times \left(\frac{5.5}{100}\right)^{2}}$$

Lleihau'r ffracsiwn \frac{25}{1000} i'r graddau lleiaf posib drwy dynnu a chanslo allan 25.

$$\sqrt{\frac{787}{16000}+0.4\times \left(\frac{1}{40}\right)^{2}+0.2\times \left(\frac{5.5}{100}\right)^{2}}$$

Cyfrifo \frac{1}{40} i bŵer 2 a chael \frac{1}{1600}.

$$\sqrt{\frac{787}{16000}+0.4\times \frac{1}{1600}+0.2\times \left(\frac{5.5}{100}\right)^{2}}$$

Lluosi 0.4 a \frac{1}{1600} i gael \frac{1}{4000}.

$$\sqrt{\frac{787}{16000}+\frac{1}{4000}+0.2\times \left(\frac{5.5}{100}\right)^{2}}$$

Adio \frac{787}{16000} a \frac{1}{4000} i gael \frac{791}{16000}.

$$\sqrt{\frac{791}{16000}+0.2\times \left(\frac{5.5}{100}\right)^{2}}$$

Ehangu \frac{5.5}{100} drwy luosi'r rhifiadur a'r enwadur gyda 10.

$$\sqrt{\frac{791}{16000}+0.2\times \left(\frac{55}{1000}\right)^{2}}$$

Lleihau'r ffracsiwn \frac{55}{1000} i'r graddau lleiaf posib drwy dynnu a chanslo allan 5.

$$\sqrt{\frac{791}{16000}+0.2\times \left(\frac{11}{200}\right)^{2}}$$

Cyfrifo \frac{11}{200} i bŵer 2 a chael \frac{121}{40000}.

$$\sqrt{\frac{791}{16000}+0.2\times \frac{121}{40000}}$$

Lluosi 0.2 a \frac{121}{40000} i gael \frac{121}{200000}.

$$\sqrt{\frac{791}{16000}+\frac{121}{200000}}$$

Adio \frac{791}{16000} a \frac{121}{200000} i gael \frac{20017}{400000}.

$$\sqrt{\frac{20017}{400000}}$$

Ailysgrifennu ail isradd y rhaniad \sqrt{\frac{20017}{400000}} fel rhaniad ail israddau \frac{\sqrt{20017}}{\sqrt{400000}}.

$$\frac{\sqrt{20017}}{\sqrt{400000}}$$

Ffactora 400000=200^{2}\times 10. Ailysgrifennu ail isradd y lluoswm \sqrt{200^{2}\times 10} fel lluoswm ail israddau \sqrt{200^{2}}\sqrt{10}. Cymryd isradd 200^{2}.

$$\frac{\sqrt{20017}}{200\sqrt{10}}$$

Mae'n rhesymoli enwadur \frac{\sqrt{20017}}{200\sqrt{10}} drwy luosi'r rhifiadur a'r enwadur â \sqrt{10}.

$$\frac{\sqrt{20017}\sqrt{10}}{200\left(\sqrt{10}\right)^{2}}$$

Sgwâr \sqrt{10} yw 10.

$$\frac{\sqrt{20017}\sqrt{10}}{200\times 10}$$

I luosi \sqrt{20017} a \sqrt{10}, dylid lluosi'r rhifau dan yr ail isradd.

$$\frac{\sqrt{200170}}{200\times 10}$$

Lluosi 200 a 10 i gael 2000.

$$\frac{\sqrt{200170}}{2000}$$