Lahenda sqrt{4/3*55*10^-9*667*10^-11*314}

$$\sqrt { \frac { 4 } { 3 } \times 55 \times 10 ^ { - 9 } \times 667 \times 10 ^ { - 11 } \times 314 }$$

Arvuta

$$\frac{\sqrt{34557270}}{15000000000}\approx 0,000000392$$

Lahenduse etapid

Sama alusega astmete korrutamiseks liitke astendajad. Liitke -9 ja -11, et saada -20.

$$\sqrt{\frac{4}{3}\times 55\times 10^{-20}\times 667\times 314}$$

Korrutage \frac{4}{3} ja 55, et leida \frac{220}{3}.

$$\sqrt{\frac{220}{3}\times 10^{-20}\times 667\times 314}$$

Arvutage -20 aste 10 ja leidke \frac{1}{100000000000000000000}.

$$\sqrt{\frac{220}{3}\times \frac{1}{100000000000000000000}\times 667\times 314}$$

Korrutage \frac{220}{3} ja \frac{1}{100000000000000000000}, et leida \frac{11}{15000000000000000000}.

$$\sqrt{\frac{11}{15000000000000000000}\times 667\times 314}$$

Korrutage \frac{11}{15000000000000000000} ja 667, et leida \frac{7337}{15000000000000000000}.

$$\sqrt{\frac{7337}{15000000000000000000}\times 314}$$

Korrutage \frac{7337}{15000000000000000000} ja 314, et leida \frac{1151909}{7500000000000000000}.

$$\sqrt{\frac{1151909}{7500000000000000000}}$$

Kirjutage: allüksus \sqrt{\frac{1151909}{7500000000000000000}}: allüksus juured \frac{\sqrt{1151909}}{\sqrt{7500000000000000000}}.

$$\frac{\sqrt{1151909}}{\sqrt{7500000000000000000}}$$

Tegurda 7500000000000000000=500000000^{2}\times 30. Kirjutage \sqrt{500000000^{2}\times 30} toote juured, kui see ruut \sqrt{500000000^{2}}\sqrt{30}. Leidke 500000000^{2} ruutjuur.

$$\frac{\sqrt{1151909}}{500000000\sqrt{30}}$$

Ratsionaliseerige korrutades lugeja ja \sqrt{30} nimetaja \frac{\sqrt{1151909}}{500000000\sqrt{30}} nimetaja.

$$\frac{\sqrt{1151909}\sqrt{30}}{500000000\left(\sqrt{30}\right)^{2}}$$

\sqrt{30} ruut on 30.

$$\frac{\sqrt{1151909}\sqrt{30}}{500000000\times 30}$$

\sqrt{1151909} ja \sqrt{30} korrutage numbrid, mis on sama juur.

$$\frac{\sqrt{34557270}}{500000000\times 30}$$

Korrutage 500000000 ja 30, et leida 15000000000.

$$\frac{\sqrt{34557270}}{15000000000}$$