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

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

Arvuta

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

Lahenduse etapid

Kirjutage: allüksus \sqrt{\frac{2015}{2016}}: allüksus juured \frac{\sqrt{2015}}{\sqrt{2016}}.

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

Tegurda 2016=12^{2}\times 14. Kirjutage \sqrt{12^{2}\times 14} toote juured, kui see ruut \sqrt{12^{2}}\sqrt{14}. Leidke 12^{2} ruutjuur.

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

Ratsionaliseerige korrutades lugeja ja \sqrt{14} nimetaja \frac{\sqrt{2015}}{12\sqrt{14}} nimetaja.

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

\sqrt{14} ruut on 14.

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

\sqrt{2015} ja \sqrt{14} korrutage numbrid, mis on sama juur.

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

Korrutage 12 ja 14, et leida 168.

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

Kirjutage: allüksus \sqrt{\frac{2016}{2017}}: allüksus juured \frac{\sqrt{2016}}{\sqrt{2017}}.

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

Tegurda 2016=12^{2}\times 14. Kirjutage \sqrt{12^{2}\times 14} toote juured, kui see ruut \sqrt{12^{2}}\sqrt{14}. Leidke 12^{2} ruutjuur.

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

Ratsionaliseerige korrutades lugeja ja \sqrt{2017} nimetaja \frac{12\sqrt{14}}{\sqrt{2017}} nimetaja.

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

\sqrt{2017} ruut on 2017.

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

\sqrt{14} ja \sqrt{2017} korrutage numbrid, mis on sama juur.

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

Jagage \frac{\sqrt{28210}}{168} väärtusega \frac{12\sqrt{28238}}{2017}, korrutades \frac{\sqrt{28210}}{168} väärtuse \frac{12\sqrt{28238}}{2017} pöördväärtusega.

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

Ratsionaliseerige korrutades lugeja ja \sqrt{28238} nimetaja \frac{\sqrt{28210}\times 2017}{168\times 12\sqrt{28238}} nimetaja.

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

\sqrt{28238} ruut on 28238.

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

\sqrt{28210} ja \sqrt{28238} korrutage numbrid, mis on sama juur.

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

Korrutage 168 ja 12, et leida 2016.

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

Korrutage 2016 ja 28238, et leida 56927808.

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

Tegurda 796593980=14^{2}\times 4064255. Kirjutage \sqrt{14^{2}\times 4064255} toote juured, kui see ruut \sqrt{14^{2}}\sqrt{4064255}. Leidke 14^{2} ruutjuur.

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

Korrutage 14 ja 2017, et leida 28238.

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

Jagage 28238\sqrt{4064255} väärtusega 56927808, et leida \frac{1}{2016}\sqrt{4064255}.

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