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

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

Luacháil

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

Céimeanna Réitigh

Ríomh cumhacht -\frac{31}{100} de 2 agus faigh \frac{961}{10000}.

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

Méadaigh 0.1 agus \frac{961}{10000} chun \frac{961}{100000} a fháil.

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

Ríomh cumhacht -\frac{11}{100} de 2 agus faigh \frac{121}{10000}.

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

Méadaigh 0.3 agus \frac{121}{10000} chun \frac{363}{100000} a fháil.

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

Suimigh \frac{961}{100000} agus \frac{363}{100000} chun \frac{331}{25000} a fháil.

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

Laghdaigh an codán \frac{4}{100} chuig na téarmaí is ísle trí 4 a bhaint agus a chealú.

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

Ríomh cumhacht \frac{1}{25} de 2 agus faigh \frac{1}{625}.

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

Méadaigh 0.4 agus \frac{1}{625} chun \frac{2}{3125} a fháil.

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

Suimigh \frac{331}{25000} agus \frac{2}{3125} chun \frac{347}{25000} a fháil.

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

Laghdaigh an codán \frac{24}{100} chuig na téarmaí is ísle trí 4 a bhaint agus a chealú.

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

Ríomh cumhacht \frac{6}{25} de 2 agus faigh \frac{36}{625}.

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

Méadaigh 0.2 agus \frac{36}{625} chun \frac{36}{3125} a fháil.

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

Suimigh \frac{347}{25000} agus \frac{36}{3125} chun \frac{127}{5000} a fháil.

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

Athscríobh fréamh cearnach na roinnte \sqrt{\frac{127}{5000}} mar roinnt na bhfréamhacha cearnacha \frac{\sqrt{127}}{\sqrt{5000}}.

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

Fachtóirigh 5000=50^{2}\times 2. Athscríobh fréamh cearnach an toraidh \sqrt{50^{2}\times 2} mar thoradh na bhfréamhacha cearnacha \sqrt{50^{2}}\sqrt{2}. Tóg fréamh chearnach 50^{2}.

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

Iolraigh an t-uimhreoir agus an t-ainmneoir faoi \sqrt{2} chun ainmneoir \frac{\sqrt{127}}{50\sqrt{2}} a thiontú in uimhir chóimheasta.

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

Is é 2 uimhir chearnach \sqrt{2}.

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

Iolraigh na huimhreacha faoin bhfréamh cearnach chun \sqrt{127} agus \sqrt{2} a iolrú.

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

Méadaigh 50 agus 2 chun 100 a fháil.

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