Whakaoti i te sqrt{2015/2016}divsqrt{2016/2017}

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

Aromātai

$$\frac{\sqrt{4064255}}{2016}\approx 0.999999877$$

Ngā Upane Otinga

Tuhia anō te pūtake rua o te whakawehenga \sqrt{\frac{2015}{2016}} hei whakawehenga o ngā pūtake rua \frac{\sqrt{2015}}{\sqrt{2016}}.

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

Tauwehea te 2016=12^{2}\times 14. Tuhia anō te pūtake rua o te hua \sqrt{12^{2}\times 14} hei hua o ngā pūtake rua \sqrt{12^{2}}\sqrt{14}. Tuhia te pūtakerua o te 12^{2}.

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

Whakangāwaritia te tauraro o \frac{\sqrt{2015}}{12\sqrt{14}} mā te whakarea i te taurunga me te tauraro ki te \sqrt{14}.

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

Ko te pūrua o \sqrt{14} ko 14.

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

Hei whakarea \sqrt{2015} me \sqrt{14}, whakareatia ngā tau i raro i te pūtake rua.

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

Whakareatia te 12 ki te 14, ka 168.

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

Tuhia anō te pūtake rua o te whakawehenga \sqrt{\frac{2016}{2017}} hei whakawehenga o ngā pūtake rua \frac{\sqrt{2016}}{\sqrt{2017}}.

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

Tauwehea te 2016=12^{2}\times 14. Tuhia anō te pūtake rua o te hua \sqrt{12^{2}\times 14} hei hua o ngā pūtake rua \sqrt{12^{2}}\sqrt{14}. Tuhia te pūtakerua o te 12^{2}.

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

Whakangāwaritia te tauraro o \frac{12\sqrt{14}}{\sqrt{2017}} mā te whakarea i te taurunga me te tauraro ki te \sqrt{2017}.

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

Ko te pūrua o \sqrt{2017} ko 2017.

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

Hei whakarea \sqrt{14} me \sqrt{2017}, whakareatia ngā tau i raro i te pūtake rua.

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

Whakawehe \frac{\sqrt{28210}}{168} ki te \frac{12\sqrt{28238}}{2017} mā te whakarea \frac{\sqrt{28210}}{168} ki te tau huripoki o \frac{12\sqrt{28238}}{2017}.

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

Whakangāwaritia te tauraro o \frac{\sqrt{28210}\times 2017}{168\times 12\sqrt{28238}} mā te whakarea i te taurunga me te tauraro ki te \sqrt{28238}.

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

Ko te pūrua o \sqrt{28238} ko 28238.

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

Hei whakarea \sqrt{28210} me \sqrt{28238}, whakareatia ngā tau i raro i te pūtake rua.

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

Whakareatia te 168 ki te 12, ka 2016.

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

Whakareatia te 2016 ki te 28238, ka 56927808.

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

Tauwehea te 796593980=14^{2}\times 4064255. Tuhia anō te pūtake rua o te hua \sqrt{14^{2}\times 4064255} hei hua o ngā pūtake rua \sqrt{14^{2}}\sqrt{4064255}. Tuhia te pūtakerua o te 14^{2}.

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

Whakareatia te 14 ki te 2017, ka 28238.

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

Whakawehea te 28238\sqrt{4064255} ki te 56927808, kia riro ko \frac{1}{2016}\sqrt{4064255}.

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