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

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

Baholash

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

Yechim qadamlari

Surat va maxrajdagi ikkala 2 ni qisqartiring.

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

Ayni asosning daraja ko'rsatkichi bo'lish uchun maxrajning darajasini surat darajasidan bo'ling.

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

55 daraja ko‘rsatkichini 10 ga hisoblang va 10000000000000000000000000000000000000000000000000000000 ni qiymatni oling.

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

1460570000000000000000000000000000000000000000000000000000000 hosil qilish uchun 146057 va 10000000000000000000000000000000000000000000000000000000 ni ko'paytirish.

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

\frac{1460570000000000000000000000000000000000000000000000000000000}{148} ulushini 4 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

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

\sqrt{\frac{365142500000000000000000000000000000000000000000000000000000}{37}} boʻlinmasining kvadrat ildizini \frac{\sqrt{365142500000000000000000000000000000000000000000000000000000}}{\sqrt{37}} kvadrat ildizlarining boʻlinmasi sifatida qayta yozing.

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

Faktor: 365142500000000000000000000000000000000000000000000000000000=500000000000000000000000000^{2}\times 1460570. \sqrt{500000000000000000000000000^{2}\times 1460570} koʻpaytmasining kvadrat ildizini \sqrt{500000000000000000000000000^{2}}\sqrt{1460570} kvadrat ildizlarining koʻpaytmasi sifatida qayta yozing. 500000000000000000000000000^{2} ning kvadrat ildizini chiqarish.

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

\frac{500000000000000000000000000\sqrt{1460570}}{\sqrt{37}} maxrajini \sqrt{37} orqali surat va maxrajini koʻpaytirish orqali ratsionallashtiring.

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

\sqrt{37} kvadrati – 37.

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

\sqrt{1460570} va \sqrt{37} ni koʻpaytirish uchun kvadrat ildiz ichidagi sonlarni koʻpaytiring.

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