sqrt{2015/2016}divsqrt{2016/2017} eching

$$\sqrt{ \frac{ 2015 }{ 2016 } } \div \sqrt{ \frac{ 2016 }{ 2017 } }$$

Baholash

$$\frac{\sqrt{4064255}}{2016}\approx 0,999999877$$

Yechim qadamlari

\sqrt{\frac{2015}{2016}} boʻlinmasining kvadrat ildizini \frac{\sqrt{2015}}{\sqrt{2016}} kvadrat ildizlarining boʻlinmasi sifatida qayta yozing.

$$\frac{\frac{\sqrt{2015}}{\sqrt{2016}}}{\sqrt{\frac{2016}{2017}}}$$

Faktor: 2016=12^{2}\times 14. \sqrt{12^{2}\times 14} koʻpaytmasining kvadrat ildizini \sqrt{12^{2}}\sqrt{14} kvadrat ildizlarining koʻpaytmasi sifatida qayta yozing. 12^{2} ning kvadrat ildizini chiqarish.

$$\frac{\frac{\sqrt{2015}}{12\sqrt{14}}}{\sqrt{\frac{2016}{2017}}}$$

\frac{\sqrt{2015}}{12\sqrt{14}} maxrajini \sqrt{14} orqali surat va maxrajini koʻpaytirish orqali ratsionallashtiring.

$$\frac{\frac{\sqrt{2015}\sqrt{14}}{12\left(\sqrt{14}\right)^{2}}}{\sqrt{\frac{2016}{2017}}}$$

\sqrt{14} kvadrati – 14.

$$\frac{\frac{\sqrt{2015}\sqrt{14}}{12\times 14}}{\sqrt{\frac{2016}{2017}}}$$

\sqrt{2015} va \sqrt{14} ni koʻpaytirish uchun kvadrat ildiz ichidagi sonlarni koʻpaytiring.

$$\frac{\frac{\sqrt{28210}}{12\times 14}}{\sqrt{\frac{2016}{2017}}}$$

168 hosil qilish uchun 12 va 14 ni ko'paytirish.

$$\frac{\frac{\sqrt{28210}}{168}}{\sqrt{\frac{2016}{2017}}}$$

\sqrt{\frac{2016}{2017}} boʻlinmasining kvadrat ildizini \frac{\sqrt{2016}}{\sqrt{2017}} kvadrat ildizlarining boʻlinmasi sifatida qayta yozing.

$$\frac{\frac{\sqrt{28210}}{168}}{\frac{\sqrt{2016}}{\sqrt{2017}}}$$

Faktor: 2016=12^{2}\times 14. \sqrt{12^{2}\times 14} koʻpaytmasining kvadrat ildizini \sqrt{12^{2}}\sqrt{14} kvadrat ildizlarining koʻpaytmasi sifatida qayta yozing. 12^{2} ning kvadrat ildizini chiqarish.

$$\frac{\frac{\sqrt{28210}}{168}}{\frac{12\sqrt{14}}{\sqrt{2017}}}$$

\frac{12\sqrt{14}}{\sqrt{2017}} maxrajini \sqrt{2017} orqali surat va maxrajini koʻpaytirish orqali ratsionallashtiring.

$$\frac{\frac{\sqrt{28210}}{168}}{\frac{12\sqrt{14}\sqrt{2017}}{\left(\sqrt{2017}\right)^{2}}}$$

\sqrt{2017} kvadrati – 2017.

$$\frac{\frac{\sqrt{28210}}{168}}{\frac{12\sqrt{14}\sqrt{2017}}{2017}}$$

\sqrt{14} va \sqrt{2017} ni koʻpaytirish uchun kvadrat ildiz ichidagi sonlarni koʻpaytiring.

$$\frac{\frac{\sqrt{28210}}{168}}{\frac{12\sqrt{28238}}{2017}}$$

\frac{\sqrt{28210}}{168} ni \frac{12\sqrt{28238}}{2017} ga bo'lish \frac{\sqrt{28210}}{168} ga k'paytirish \frac{12\sqrt{28238}}{2017} ga qaytarish.

$$\frac{\sqrt{28210}\times 2017}{168\times 12\sqrt{28238}}$$

\frac{\sqrt{28210}\times 2017}{168\times 12\sqrt{28238}} maxrajini \sqrt{28238} orqali surat va maxrajini koʻpaytirish orqali ratsionallashtiring.

$$\frac{\sqrt{28210}\times 2017\sqrt{28238}}{168\times 12\left(\sqrt{28238}\right)^{2}}$$

\sqrt{28238} kvadrati – 28238.

$$\frac{\sqrt{28210}\times 2017\sqrt{28238}}{168\times 12\times 28238}$$

\sqrt{28210} va \sqrt{28238} ni koʻpaytirish uchun kvadrat ildiz ichidagi sonlarni koʻpaytiring.

$$\frac{\sqrt{796593980}\times 2017}{168\times 12\times 28238}$$

2016 hosil qilish uchun 168 va 12 ni ko'paytirish.

$$\frac{\sqrt{796593980}\times 2017}{2016\times 28238}$$

56927808 hosil qilish uchun 2016 va 28238 ni ko'paytirish.

$$\frac{\sqrt{796593980}\times 2017}{56927808}$$

Faktor: 796593980=14^{2}\times 4064255. \sqrt{14^{2}\times 4064255} koʻpaytmasining kvadrat ildizini \sqrt{14^{2}}\sqrt{4064255} kvadrat ildizlarining koʻpaytmasi sifatida qayta yozing. 14^{2} ning kvadrat ildizini chiqarish.

$$\frac{14\sqrt{4064255}\times 2017}{56927808}$$

28238 hosil qilish uchun 14 va 2017 ni ko'paytirish.

$$\frac{28238\sqrt{4064255}}{56927808}$$

\frac{1}{2016}\sqrt{4064255} ni olish uchun 28238\sqrt{4064255} ni 56927808 ga bo‘ling.

$$\frac{1}{2016}\sqrt{4064255}$$