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

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

Calcola

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

Procedura della soluzione

Cancella 2 nel numeratore e nel denominatore.

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

Per dividere potenze della stessa base, sottrai l'esponente del denominatore dall'esponente del numeratore.

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

Calcola 10 alla potenza di 55 e ottieni 10000000000000000000000000000000000000000000000000000000.

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

Moltiplica 146057 e 10000000000000000000000000000000000000000000000000000000 per ottenere 1460570000000000000000000000000000000000000000000000000000000.

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

Riduci la frazione \frac{1460570000000000000000000000000000000000000000000000000000000}{148} ai minimi termini estraendo e annullando 4.

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

Riscrivi la radice quadrata del \sqrt{\frac{365142500000000000000000000000000000000000000000000000000000}{37}} di divisione come divisione delle radici quadrate \frac{\sqrt{365142500000000000000000000000000000000000000000000000000000}}{\sqrt{37}}.

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

Fattorizzare 365142500000000000000000000000000000000000000000000000000000=500000000000000000000000000^{2}\times 1460570. Riscrivi la radice quadrata del prodotto \sqrt{500000000000000000000000000^{2}\times 1460570} come prodotto di radici quadrate \sqrt{500000000000000000000000000^{2}}\sqrt{1460570}. Calcola la radice quadrata di 500000000000000000000000000^{2}.

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

Razionalizza il denominatore di \frac{500000000000000000000000000\sqrt{1460570}}{\sqrt{37}} moltiplicando il numeratore e il denominatore per \sqrt{37}.

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

Il quadrato di \sqrt{37} è 37.

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

Per moltiplicare \sqrt{1460570} e \sqrt{37}, moltiplica i numeri sotto la radice quadrata.

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