Whakaoti i te sqrt{0.1(-14.5%)^2+0.3(-2.5%)^2+0.4(2.5%)^2+0.2(5.5%)^2}

$$\sqrt { 0.1 ( - 14.5 \% ) ^ { 2 } + 0.3 ( - 2.5 \% ) ^ { 2 } + 0.4 ( 2.5 \% ) ^ { 2 } + 0.2 ( 5.5 \% ) ^ { 2 } }$$

Aromātai

$$\frac{\sqrt{3145}}{1000}\approx 0.0560803$$

Ngā Upane Otinga

Whakarohaina te \frac{14.5}{100} mā te whakarea i te taurunga me te tauraro ki te 10.

$$\sqrt{0.1\left(-\frac{145}{1000}\right)^{2}+0.3\left(-\frac{2.5}{100}\right)^{2}+0.4\times \left(\frac{2.5}{100}\right)^{2}+0.2\times \left(\frac{5.5}{100}\right)^{2}}$$

Whakahekea te hautanga \frac{145}{1000} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 5.

$$\sqrt{0.1\left(-\frac{29}{200}\right)^{2}+0.3\left(-\frac{2.5}{100}\right)^{2}+0.4\times \left(\frac{2.5}{100}\right)^{2}+0.2\times \left(\frac{5.5}{100}\right)^{2}}$$

Tātaihia te -\frac{29}{200} mā te pū o 2, kia riro ko \frac{841}{40000}.

$$\sqrt{0.1\times \frac{841}{40000}+0.3\left(-\frac{2.5}{100}\right)^{2}+0.4\times \left(\frac{2.5}{100}\right)^{2}+0.2\times \left(\frac{5.5}{100}\right)^{2}}$$

Whakareatia te 0.1 ki te \frac{841}{40000}, ka \frac{841}{400000}.

$$\sqrt{\frac{841}{400000}+0.3\left(-\frac{2.5}{100}\right)^{2}+0.4\times \left(\frac{2.5}{100}\right)^{2}+0.2\times \left(\frac{5.5}{100}\right)^{2}}$$

Whakarohaina te \frac{2.5}{100} mā te whakarea i te taurunga me te tauraro ki te 10.

$$\sqrt{\frac{841}{400000}+0.3\left(-\frac{25}{1000}\right)^{2}+0.4\times \left(\frac{2.5}{100}\right)^{2}+0.2\times \left(\frac{5.5}{100}\right)^{2}}$$

Whakahekea te hautanga \frac{25}{1000} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 25.

$$\sqrt{\frac{841}{400000}+0.3\left(-\frac{1}{40}\right)^{2}+0.4\times \left(\frac{2.5}{100}\right)^{2}+0.2\times \left(\frac{5.5}{100}\right)^{2}}$$

Tātaihia te -\frac{1}{40} mā te pū o 2, kia riro ko \frac{1}{1600}.

$$\sqrt{\frac{841}{400000}+0.3\times \frac{1}{1600}+0.4\times \left(\frac{2.5}{100}\right)^{2}+0.2\times \left(\frac{5.5}{100}\right)^{2}}$$

Whakareatia te 0.3 ki te \frac{1}{1600}, ka \frac{3}{16000}.

$$\sqrt{\frac{841}{400000}+\frac{3}{16000}+0.4\times \left(\frac{2.5}{100}\right)^{2}+0.2\times \left(\frac{5.5}{100}\right)^{2}}$$

Tāpirihia te \frac{841}{400000} ki te \frac{3}{16000}, ka \frac{229}{100000}.

$$\sqrt{\frac{229}{100000}+0.4\times \left(\frac{2.5}{100}\right)^{2}+0.2\times \left(\frac{5.5}{100}\right)^{2}}$$

Whakarohaina te \frac{2.5}{100} mā te whakarea i te taurunga me te tauraro ki te 10.

$$\sqrt{\frac{229}{100000}+0.4\times \left(\frac{25}{1000}\right)^{2}+0.2\times \left(\frac{5.5}{100}\right)^{2}}$$

Whakahekea te hautanga \frac{25}{1000} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 25.

$$\sqrt{\frac{229}{100000}+0.4\times \left(\frac{1}{40}\right)^{2}+0.2\times \left(\frac{5.5}{100}\right)^{2}}$$

Tātaihia te \frac{1}{40} mā te pū o 2, kia riro ko \frac{1}{1600}.

$$\sqrt{\frac{229}{100000}+0.4\times \frac{1}{1600}+0.2\times \left(\frac{5.5}{100}\right)^{2}}$$

Whakareatia te 0.4 ki te \frac{1}{1600}, ka \frac{1}{4000}.

$$\sqrt{\frac{229}{100000}+\frac{1}{4000}+0.2\times \left(\frac{5.5}{100}\right)^{2}}$$

Tāpirihia te \frac{229}{100000} ki te \frac{1}{4000}, ka \frac{127}{50000}.

$$\sqrt{\frac{127}{50000}+0.2\times \left(\frac{5.5}{100}\right)^{2}}$$

Whakarohaina te \frac{5.5}{100} mā te whakarea i te taurunga me te tauraro ki te 10.

$$\sqrt{\frac{127}{50000}+0.2\times \left(\frac{55}{1000}\right)^{2}}$$

Whakahekea te hautanga \frac{55}{1000} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 5.

$$\sqrt{\frac{127}{50000}+0.2\times \left(\frac{11}{200}\right)^{2}}$$

Tātaihia te \frac{11}{200} mā te pū o 2, kia riro ko \frac{121}{40000}.

$$\sqrt{\frac{127}{50000}+0.2\times \frac{121}{40000}}$$

Whakareatia te 0.2 ki te \frac{121}{40000}, ka \frac{121}{200000}.

$$\sqrt{\frac{127}{50000}+\frac{121}{200000}}$$

Tāpirihia te \frac{127}{50000} ki te \frac{121}{200000}, ka \frac{629}{200000}.

$$\sqrt{\frac{629}{200000}}$$

Tuhia anō te pūtake rua o te whakawehenga \sqrt{\frac{629}{200000}} hei whakawehenga o ngā pūtake rua \frac{\sqrt{629}}{\sqrt{200000}}.

$$\frac{\sqrt{629}}{\sqrt{200000}}$$

Tauwehea te 200000=200^{2}\times 5. Tuhia anō te pūtake rua o te hua \sqrt{200^{2}\times 5} hei hua o ngā pūtake rua \sqrt{200^{2}}\sqrt{5}. Tuhia te pūtakerua o te 200^{2}.

$$\frac{\sqrt{629}}{200\sqrt{5}}$$

Whakangāwaritia te tauraro o \frac{\sqrt{629}}{200\sqrt{5}} mā te whakarea i te taurunga me te tauraro ki te \sqrt{5}.

$$\frac{\sqrt{629}\sqrt{5}}{200\left(\sqrt{5}\right)^{2}}$$

Ko te pūrua o \sqrt{5} ko 5.

$$\frac{\sqrt{629}\sqrt{5}}{200\times 5}$$

Hei whakarea \sqrt{629} me \sqrt{5}, whakareatia ngā tau i raro i te pūtake rua.

$$\frac{\sqrt{3145}}{200\times 5}$$

Whakareatia te 200 ki te 5, ka 1000.

$$\frac{\sqrt{3145}}{1000}$$