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

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

Aromātai

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

Ngā Upane Otinga

Tātaihia te -\frac{31}{100} mā te pū o 2, kia riro ko \frac{961}{10000}.

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

Whakareatia te 0.1 ki te \frac{961}{10000}, ka \frac{961}{100000}.

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

Tātaihia te -\frac{11}{100} mā te pū o 2, kia riro ko \frac{121}{10000}.

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

Whakareatia te 0.3 ki te \frac{121}{10000}, ka \frac{363}{100000}.

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

Tāpirihia te \frac{961}{100000} ki te \frac{363}{100000}, ka \frac{331}{25000}.

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

Whakahekea te hautanga \frac{4}{100} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 4.

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

Tātaihia te \frac{1}{25} mā te pū o 2, kia riro ko \frac{1}{625}.

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

Whakareatia te 0.4 ki te \frac{1}{625}, ka \frac{2}{3125}.

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

Tāpirihia te \frac{331}{25000} ki te \frac{2}{3125}, ka \frac{347}{25000}.

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

Whakahekea te hautanga \frac{24}{100} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 4.

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

Tātaihia te \frac{6}{25} mā te pū o 2, kia riro ko \frac{36}{625}.

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

Whakareatia te 0.2 ki te \frac{36}{625}, ka \frac{36}{3125}.

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

Tāpirihia te \frac{347}{25000} ki te \frac{36}{3125}, ka \frac{127}{5000}.

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

Tuhia anō te pūtake rua o te whakawehenga \sqrt{\frac{127}{5000}} hei whakawehenga o ngā pūtake rua \frac{\sqrt{127}}{\sqrt{5000}}.

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

Tauwehea te 5000=50^{2}\times 2. Tuhia anō te pūtake rua o te hua \sqrt{50^{2}\times 2} hei hua o ngā pūtake rua \sqrt{50^{2}}\sqrt{2}. Tuhia te pūtakerua o te 50^{2}.

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

Whakangāwaritia te tauraro o \frac{\sqrt{127}}{50\sqrt{2}} mā te whakarea i te taurunga me te tauraro ki te \sqrt{2}.

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

Ko te pūrua o \sqrt{2} ko 2.

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

Hei whakarea \sqrt{127} me \sqrt{2}, whakareatia ngā tau i raro i te pūtake rua.

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

Whakareatia te 50 ki te 2, ka 100.

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