{left(77/89xsqrt{45(6)2}right)}^2 eching

$${ \left(7 \frac{ 7 }{ 89x \sqrt{ 45(6)2 } } \right) }^{ 2 }$$

Baholash

$$\frac{2401}{4277340x^{2}}$$

Yechim qadamlari

270 hosil qilish uchun 45 va 6 ni ko'paytirish.

$$\left(7\times \frac{7}{89x\sqrt{270\times 2}}\right)^{2}$$

540 hosil qilish uchun 270 va 2 ni ko'paytirish.

$$\left(7\times \frac{7}{89x\sqrt{540}}\right)^{2}$$

Faktor: 540=6^{2}\times 15. \sqrt{6^{2}\times 15} koʻpaytmasining kvadrat ildizini \sqrt{6^{2}}\sqrt{15} kvadrat ildizlarining koʻpaytmasi sifatida qayta yozing. 6^{2} ning kvadrat ildizini chiqarish.

$$\left(7\times \frac{7}{89x\times 6\sqrt{15}}\right)^{2}$$

534 hosil qilish uchun 89 va 6 ni ko'paytirish.

$$\left(7\times \frac{7}{534x\sqrt{15}}\right)^{2}$$

\frac{7}{534x\sqrt{15}} maxrajini \sqrt{15} orqali surat va maxrajini koʻpaytirish orqali ratsionallashtiring.

$$\left(7\times \frac{7\sqrt{15}}{534x\left(\sqrt{15}\right)^{2}}\right)^{2}$$

\sqrt{15} kvadrati – 15.

$$\left(7\times \frac{7\sqrt{15}}{534x\times 15}\right)^{2}$$

8010 hosil qilish uchun 534 va 15 ni ko'paytirish.

$$\left(7\times \frac{7\sqrt{15}}{8010x}\right)^{2}$$

7\times \frac{7\sqrt{15}}{8010x} ni yagona kasrga aylantiring.

$$\left(\frac{7\times 7\sqrt{15}}{8010x}\right)^{2}$$

\frac{7\times 7\sqrt{15}}{8010x}ni darajaga oshirish uchun, surat va maxrajni darajaga oshirib, keyin bo‘ling.

$$\frac{\left(7\times 7\sqrt{15}\right)^{2}}{\left(8010x\right)^{2}}$$

49 hosil qilish uchun 7 va 7 ni ko'paytirish.

$$\frac{\left(49\sqrt{15}\right)^{2}}{\left(8010x\right)^{2}}$$

\left(49\sqrt{15}\right)^{2} ni kengaytirish.

$$\frac{49^{2}\left(\sqrt{15}\right)^{2}}{\left(8010x\right)^{2}}$$

2 daraja ko‘rsatkichini 49 ga hisoblang va 2401 ni qiymatni oling.

$$\frac{2401\left(\sqrt{15}\right)^{2}}{\left(8010x\right)^{2}}$$

\sqrt{15} kvadrati – 15.

$$\frac{2401\times 15}{\left(8010x\right)^{2}}$$

36015 hosil qilish uchun 2401 va 15 ni ko'paytirish.

$$\frac{36015}{\left(8010x\right)^{2}}$$

\left(8010x\right)^{2} ni kengaytirish.

$$\frac{36015}{8010^{2}x^{2}}$$

2 daraja ko‘rsatkichini 8010 ga hisoblang va 64160100 ni qiymatni oling.

$$\frac{36015}{64160100x^{2}}$$

Kengaytirish

$$\frac{2401}{4277340x^{2}}$$

Yechim qadamlari

270 hosil qilish uchun 45 va 6 ni ko'paytirish.

$$\left(7\times \frac{7}{89x\sqrt{270\times 2}}\right)^{2}$$

540 hosil qilish uchun 270 va 2 ni ko'paytirish.

$$\left(7\times \frac{7}{89x\sqrt{540}}\right)^{2}$$

Faktor: 540=6^{2}\times 15. \sqrt{6^{2}\times 15} koʻpaytmasining kvadrat ildizini \sqrt{6^{2}}\sqrt{15} kvadrat ildizlarining koʻpaytmasi sifatida qayta yozing. 6^{2} ning kvadrat ildizini chiqarish.

$$\left(7\times \frac{7}{89x\times 6\sqrt{15}}\right)^{2}$$

534 hosil qilish uchun 89 va 6 ni ko'paytirish.

$$\left(7\times \frac{7}{534x\sqrt{15}}\right)^{2}$$

\frac{7}{534x\sqrt{15}} maxrajini \sqrt{15} orqali surat va maxrajini koʻpaytirish orqali ratsionallashtiring.

$$\left(7\times \frac{7\sqrt{15}}{534x\left(\sqrt{15}\right)^{2}}\right)^{2}$$

\sqrt{15} kvadrati – 15.

$$\left(7\times \frac{7\sqrt{15}}{534x\times 15}\right)^{2}$$

8010 hosil qilish uchun 534 va 15 ni ko'paytirish.

$$\left(7\times \frac{7\sqrt{15}}{8010x}\right)^{2}$$

7\times \frac{7\sqrt{15}}{8010x} ni yagona kasrga aylantiring.

$$\left(\frac{7\times 7\sqrt{15}}{8010x}\right)^{2}$$

\frac{7\times 7\sqrt{15}}{8010x}ni darajaga oshirish uchun, surat va maxrajni darajaga oshirib, keyin bo‘ling.

$$\frac{\left(7\times 7\sqrt{15}\right)^{2}}{\left(8010x\right)^{2}}$$

49 hosil qilish uchun 7 va 7 ni ko'paytirish.

$$\frac{\left(49\sqrt{15}\right)^{2}}{\left(8010x\right)^{2}}$$

\left(49\sqrt{15}\right)^{2} ni kengaytirish.

$$\frac{49^{2}\left(\sqrt{15}\right)^{2}}{\left(8010x\right)^{2}}$$

2 daraja ko‘rsatkichini 49 ga hisoblang va 2401 ni qiymatni oling.

$$\frac{2401\left(\sqrt{15}\right)^{2}}{\left(8010x\right)^{2}}$$

\sqrt{15} kvadrati – 15.

$$\frac{2401\times 15}{\left(8010x\right)^{2}}$$

36015 hosil qilish uchun 2401 va 15 ni ko'paytirish.

$$\frac{36015}{\left(8010x\right)^{2}}$$

\left(8010x\right)^{2} ni kengaytirish.

$$\frac{36015}{8010^{2}x^{2}}$$

2 daraja ko‘rsatkichini 8010 ga hisoblang va 64160100 ni qiymatni oling.

$$\frac{36015}{64160100x^{2}}$$