Lahenda sqrt{292114*10^36/296*10^-19}

$$\sqrt{ \frac{ 292114 \times { 10 }^{ 36 } }{ 296 \times { 10 }^{ -19 } } }$$

Arvuta

$$\frac{500000000000000000000000000\sqrt{54041090}}{37}\approx 9,934141239 \cdot 10^{28}$$

Lahenduse etapid

Taandage 2 nii lugejas kui ka nimetajas.

$$\sqrt{\frac{146057\times 10^{36}}{148\times 10^{-19}}}$$

Sama alusega astmete jagamiseks lahutage nimetaja astendaja lugeja astendajast.

$$\sqrt{\frac{146057\times 10^{55}}{148}}$$

Arvutage 55 aste 10 ja leidke 10000000000000000000000000000000000000000000000000000000.

$$\sqrt{\frac{146057\times 10000000000000000000000000000000000000000000000000000000}{148}}$$

Korrutage 146057 ja 10000000000000000000000000000000000000000000000000000000, et leida 1460570000000000000000000000000000000000000000000000000000000.

$$\sqrt{\frac{1460570000000000000000000000000000000000000000000000000000000}{148}}$$

Taandage murd \frac{1460570000000000000000000000000000000000000000000000000000000}{148} vähimale ühiskordsele, eraldades ja taandades arvu 4.

$$\sqrt{\frac{365142500000000000000000000000000000000000000000000000000000}{37}}$$

Kirjutage: allüksus \sqrt{\frac{365142500000000000000000000000000000000000000000000000000000}{37}}: allüksus juured \frac{\sqrt{365142500000000000000000000000000000000000000000000000000000}}{\sqrt{37}}.

$$\frac{\sqrt{365142500000000000000000000000000000000000000000000000000000}}{\sqrt{37}}$$

Tegurda 365142500000000000000000000000000000000000000000000000000000=500000000000000000000000000^{2}\times 1460570. Kirjutage \sqrt{500000000000000000000000000^{2}\times 1460570} toote juured, kui see ruut \sqrt{500000000000000000000000000^{2}}\sqrt{1460570}. Leidke 500000000000000000000000000^{2} ruutjuur.

$$\frac{500000000000000000000000000\sqrt{1460570}}{\sqrt{37}}$$

Ratsionaliseerige korrutades lugeja ja \sqrt{37} nimetaja \frac{500000000000000000000000000\sqrt{1460570}}{\sqrt{37}} nimetaja.

$$\frac{500000000000000000000000000\sqrt{1460570}\sqrt{37}}{\left(\sqrt{37}\right)^{2}}$$

\sqrt{37} ruut on 37.

$$\frac{500000000000000000000000000\sqrt{1460570}\sqrt{37}}{37}$$

\sqrt{1460570} ja \sqrt{37} korrutage numbrid, mis on sama juur.

$$\frac{500000000000000000000000000\sqrt{54041090}}{37}$$