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

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

Evalwa

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

Passi tas-Soluzzjonijiet

Espandi \frac{14.5}{100} billi timmultiplika kemm in-numeratur kif ukoll id-denominatur b'10.

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

Naqqas il-frazzjoni \frac{145}{1000} għat-termini l-aktar baxxi billi testratta u tikkanċella barra 5.

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

Ikkalkula -\frac{29}{200} bil-power ta' 2 u tikseb \frac{841}{40000}.

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

Immultiplika 0.1 u \frac{841}{40000} biex tikseb \frac{841}{400000}.

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

Espandi \frac{2.5}{100} billi timmultiplika kemm in-numeratur kif ukoll id-denominatur b'10.

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

Naqqas il-frazzjoni \frac{25}{1000} għat-termini l-aktar baxxi billi testratta u tikkanċella barra 25.

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

Ikkalkula -\frac{1}{40} bil-power ta' 2 u tikseb \frac{1}{1600}.

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

Immultiplika 0.3 u \frac{1}{1600} biex tikseb \frac{3}{16000}.

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

Żid \frac{841}{400000} u \frac{3}{16000} biex tikseb \frac{229}{100000}.

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

Espandi \frac{2.5}{100} billi timmultiplika kemm in-numeratur kif ukoll id-denominatur b'10.

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

Naqqas il-frazzjoni \frac{25}{1000} għat-termini l-aktar baxxi billi testratta u tikkanċella barra 25.

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

Ikkalkula \frac{1}{40} bil-power ta' 2 u tikseb \frac{1}{1600}.

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

Immultiplika 0.4 u \frac{1}{1600} biex tikseb \frac{1}{4000}.

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

Żid \frac{229}{100000} u \frac{1}{4000} biex tikseb \frac{127}{50000}.

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

Espandi \frac{5.5}{100} billi timmultiplika kemm in-numeratur kif ukoll id-denominatur b'10.

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

Naqqas il-frazzjoni \frac{55}{1000} għat-termini l-aktar baxxi billi testratta u tikkanċella barra 5.

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

Ikkalkula \frac{11}{200} bil-power ta' 2 u tikseb \frac{121}{40000}.

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

Immultiplika 0.2 u \frac{121}{40000} biex tikseb \frac{121}{200000}.

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

Żid \frac{127}{50000} u \frac{121}{200000} biex tikseb \frac{629}{200000}.

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

Erġa' ikteb id-diviżjoni tal-għerq kwadrat \sqrt{\frac{629}{200000}} bħala d-diviżjoni tal-għeruq kwadrati \frac{\sqrt{629}}{\sqrt{200000}}.

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

Iffattura 200000=200^{2}\times 5. Erġa' ikteb l-għerq kwadrat tal-prodott \sqrt{200^{2}\times 5} bħala l-prodott tal-għeruq kwadrati \sqrt{200^{2}}\sqrt{5}. Ħu l-għerq kwadrat ta' 200^{2}.

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

Irrazzjonalizza d-denominatur tal-\frac{\sqrt{629}}{200\sqrt{5}} billi timmultiplika in-numeratur u d-denominatur mill-\sqrt{5}.

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

Il-kwadrat ta' \sqrt{5} huwa 5.

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

Biex timmultiplika \sqrt{629} u \sqrt{5}, immultiplika n-numri taħt l-għerq kwadrat.

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

Immultiplika 200 u 5 biex tikseb 1000.

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