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

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

Evalwa

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

Passi tas-Soluzzjonijiet

Erġa' ikteb id-diviżjoni tal-għerq kwadrat \sqrt{\frac{2015}{2016}} bħala d-diviżjoni tal-għeruq kwadrati \frac{\sqrt{2015}}{\sqrt{2016}}.

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

Iffattura 2016=12^{2}\times 14. Erġa' ikteb l-għerq kwadrat tal-prodott \sqrt{12^{2}\times 14} bħala l-prodott tal-għeruq kwadrati \sqrt{12^{2}}\sqrt{14}. Ħu l-għerq kwadrat ta' 12^{2}.

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

Irrazzjonalizza d-denominatur tal-\frac{\sqrt{2015}}{12\sqrt{14}} billi timmultiplika in-numeratur u d-denominatur mill-\sqrt{14}.

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

Il-kwadrat ta' \sqrt{14} huwa 14.

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

Biex timmultiplika \sqrt{2015} u \sqrt{14}, immultiplika n-numri taħt l-għerq kwadrat.

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

Immultiplika 12 u 14 biex tikseb 168.

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

Erġa' ikteb id-diviżjoni tal-għerq kwadrat \sqrt{\frac{2016}{2017}} bħala d-diviżjoni tal-għeruq kwadrati \frac{\sqrt{2016}}{\sqrt{2017}}.

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

Iffattura 2016=12^{2}\times 14. Erġa' ikteb l-għerq kwadrat tal-prodott \sqrt{12^{2}\times 14} bħala l-prodott tal-għeruq kwadrati \sqrt{12^{2}}\sqrt{14}. Ħu l-għerq kwadrat ta' 12^{2}.

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

Irrazzjonalizza d-denominatur tal-\frac{12\sqrt{14}}{\sqrt{2017}} billi timmultiplika in-numeratur u d-denominatur mill-\sqrt{2017}.

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

Il-kwadrat ta' \sqrt{2017} huwa 2017.

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

Biex timmultiplika \sqrt{14} u \sqrt{2017}, immultiplika n-numri taħt l-għerq kwadrat.

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

Iddividi \frac{\sqrt{28210}}{168} b'\frac{12\sqrt{28238}}{2017} billi timmultiplika \frac{\sqrt{28210}}{168} bir-reċiproku ta' \frac{12\sqrt{28238}}{2017}.

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

Irrazzjonalizza d-denominatur tal-\frac{\sqrt{28210}\times 2017}{168\times 12\sqrt{28238}} billi timmultiplika in-numeratur u d-denominatur mill-\sqrt{28238}.

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

Il-kwadrat ta' \sqrt{28238} huwa 28238.

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

Biex timmultiplika \sqrt{28210} u \sqrt{28238}, immultiplika n-numri taħt l-għerq kwadrat.

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

Immultiplika 168 u 12 biex tikseb 2016.

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

Immultiplika 2016 u 28238 biex tikseb 56927808.

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

Iffattura 796593980=14^{2}\times 4064255. Erġa' ikteb l-għerq kwadrat tal-prodott \sqrt{14^{2}\times 4064255} bħala l-prodott tal-għeruq kwadrati \sqrt{14^{2}}\sqrt{4064255}. Ħu l-għerq kwadrat ta' 14^{2}.

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

Immultiplika 14 u 2017 biex tikseb 28238.

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

Iddividi 28238\sqrt{4064255} b'56927808 biex tikseb\frac{1}{2016}\sqrt{4064255}.

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