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

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

Luacháil

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

Céimeanna Réitigh

Laghdaigh an codán \frac{5}{100} chuig na téarmaí is ísle trí 5 a bhaint agus a chealú.

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

Méadaigh -14 agus \frac{1}{20} chun -\frac{7}{10} a fháil.

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

Ríomh cumhacht -\frac{7}{10} de 2 agus faigh \frac{49}{100}.

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

Méadaigh 0.1 agus \frac{49}{100} chun \frac{49}{1000} a fháil.

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

Fairsingigh \frac{2.5}{100} tríd an t-uimhreoir agus an t-ainmneoir araon a iolrú faoi 10.

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

Laghdaigh an codán \frac{25}{1000} chuig na téarmaí is ísle trí 25 a bhaint agus a chealú.

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

Ríomh cumhacht -\frac{1}{40} de 2 agus faigh \frac{1}{1600}.

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

Méadaigh 0.3 agus \frac{1}{1600} chun \frac{3}{16000} a fháil.

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

Suimigh \frac{49}{1000} agus \frac{3}{16000} chun \frac{787}{16000} a fháil.

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

Fairsingigh \frac{2.5}{100} tríd an t-uimhreoir agus an t-ainmneoir araon a iolrú faoi 10.

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

Laghdaigh an codán \frac{25}{1000} chuig na téarmaí is ísle trí 25 a bhaint agus a chealú.

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

Ríomh cumhacht \frac{1}{40} de 2 agus faigh \frac{1}{1600}.

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

Méadaigh 0.4 agus \frac{1}{1600} chun \frac{1}{4000} a fháil.

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

Suimigh \frac{787}{16000} agus \frac{1}{4000} chun \frac{791}{16000} a fháil.

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

Fairsingigh \frac{5.5}{100} tríd an t-uimhreoir agus an t-ainmneoir araon a iolrú faoi 10.

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

Laghdaigh an codán \frac{55}{1000} chuig na téarmaí is ísle trí 5 a bhaint agus a chealú.

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

Ríomh cumhacht \frac{11}{200} de 2 agus faigh \frac{121}{40000}.

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

Méadaigh 0.2 agus \frac{121}{40000} chun \frac{121}{200000} a fháil.

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

Suimigh \frac{791}{16000} agus \frac{121}{200000} chun \frac{20017}{400000} a fháil.

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

Athscríobh fréamh cearnach na roinnte \sqrt{\frac{20017}{400000}} mar roinnt na bhfréamhacha cearnacha \frac{\sqrt{20017}}{\sqrt{400000}}.

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

Fachtóirigh 400000=200^{2}\times 10. Athscríobh fréamh cearnach an toraidh \sqrt{200^{2}\times 10} mar thoradh na bhfréamhacha cearnacha \sqrt{200^{2}}\sqrt{10}. Tóg fréamh chearnach 200^{2}.

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

Iolraigh an t-uimhreoir agus an t-ainmneoir faoi \sqrt{10} chun ainmneoir \frac{\sqrt{20017}}{200\sqrt{10}} a thiontú in uimhir chóimheasta.

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

Is é 10 uimhir chearnach \sqrt{10}.

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

Iolraigh na huimhreacha faoin bhfréamh cearnach chun \sqrt{20017} agus \sqrt{10} a iolrú.

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

Méadaigh 200 agus 10 chun 2000 a fháil.

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