Datrys sqrt{0.1(-31%)^2+0.3(-11%)^2+0.4(4%)^2+0.2(24%)^2}

$$\sqrt { 0.1 ( - 31 \% ) ^ { 2 } + 0.3 ( - 11 \% ) ^ { 2 } + 0.4 ( 4 \% ) ^ { 2 } + 0.2 ( 24 \% ) ^ { 2 } }$$

Enrhifo

$$\frac{\sqrt{254}}{100}\approx 0.159373775$$

Camau Ateb

Cyfrifo -\frac{31}{100} i bŵer 2 a chael \frac{961}{10000}.

$$\sqrt{0.1\times \frac{961}{10000}+0.3\left(-\frac{11}{100}\right)^{2}+0.4\times \left(\frac{4}{100}\right)^{2}+0.2\times \left(\frac{24}{100}\right)^{2}}$$

Lluosi 0.1 a \frac{961}{10000} i gael \frac{961}{100000}.

$$\sqrt{\frac{961}{100000}+0.3\left(-\frac{11}{100}\right)^{2}+0.4\times \left(\frac{4}{100}\right)^{2}+0.2\times \left(\frac{24}{100}\right)^{2}}$$

Cyfrifo -\frac{11}{100} i bŵer 2 a chael \frac{121}{10000}.

$$\sqrt{\frac{961}{100000}+0.3\times \frac{121}{10000}+0.4\times \left(\frac{4}{100}\right)^{2}+0.2\times \left(\frac{24}{100}\right)^{2}}$$

Lluosi 0.3 a \frac{121}{10000} i gael \frac{363}{100000}.

$$\sqrt{\frac{961}{100000}+\frac{363}{100000}+0.4\times \left(\frac{4}{100}\right)^{2}+0.2\times \left(\frac{24}{100}\right)^{2}}$$

Adio \frac{961}{100000} a \frac{363}{100000} i gael \frac{331}{25000}.

$$\sqrt{\frac{331}{25000}+0.4\times \left(\frac{4}{100}\right)^{2}+0.2\times \left(\frac{24}{100}\right)^{2}}$$

Lleihau'r ffracsiwn \frac{4}{100} i'r graddau lleiaf posib drwy dynnu a chanslo allan 4.

$$\sqrt{\frac{331}{25000}+0.4\times \left(\frac{1}{25}\right)^{2}+0.2\times \left(\frac{24}{100}\right)^{2}}$$

Cyfrifo \frac{1}{25} i bŵer 2 a chael \frac{1}{625}.

$$\sqrt{\frac{331}{25000}+0.4\times \frac{1}{625}+0.2\times \left(\frac{24}{100}\right)^{2}}$$

Lluosi 0.4 a \frac{1}{625} i gael \frac{2}{3125}.

$$\sqrt{\frac{331}{25000}+\frac{2}{3125}+0.2\times \left(\frac{24}{100}\right)^{2}}$$

Adio \frac{331}{25000} a \frac{2}{3125} i gael \frac{347}{25000}.

$$\sqrt{\frac{347}{25000}+0.2\times \left(\frac{24}{100}\right)^{2}}$$

Lleihau'r ffracsiwn \frac{24}{100} i'r graddau lleiaf posib drwy dynnu a chanslo allan 4.

$$\sqrt{\frac{347}{25000}+0.2\times \left(\frac{6}{25}\right)^{2}}$$

Cyfrifo \frac{6}{25} i bŵer 2 a chael \frac{36}{625}.

$$\sqrt{\frac{347}{25000}+0.2\times \frac{36}{625}}$$

Lluosi 0.2 a \frac{36}{625} i gael \frac{36}{3125}.

$$\sqrt{\frac{347}{25000}+\frac{36}{3125}}$$

Adio \frac{347}{25000} a \frac{36}{3125} i gael \frac{127}{5000}.

$$\sqrt{\frac{127}{5000}}$$

Ailysgrifennu ail isradd y rhaniad \sqrt{\frac{127}{5000}} fel rhaniad ail israddau \frac{\sqrt{127}}{\sqrt{5000}}.

$$\frac{\sqrt{127}}{\sqrt{5000}}$$

Ffactora 5000=50^{2}\times 2. Ailysgrifennu ail isradd y lluoswm \sqrt{50^{2}\times 2} fel lluoswm ail israddau \sqrt{50^{2}}\sqrt{2}. Cymryd isradd 50^{2}.

$$\frac{\sqrt{127}}{50\sqrt{2}}$$

Mae'n rhesymoli enwadur \frac{\sqrt{127}}{50\sqrt{2}} drwy luosi'r rhifiadur a'r enwadur â \sqrt{2}.

$$\frac{\sqrt{127}\sqrt{2}}{50\left(\sqrt{2}\right)^{2}}$$

Sgwâr \sqrt{2} yw 2.

$$\frac{\sqrt{127}\sqrt{2}}{50\times 2}$$

I luosi \sqrt{127} a \sqrt{2}, dylid lluosi'r rhifau dan yr ail isradd.

$$\frac{\sqrt{254}}{50\times 2}$$

Lluosi 50 a 2 i gael 100.

$$\frac{\sqrt{254}}{100}$$