Whakaoti i te r=10*535134-2217*2489/sqrt{10*695135-(2489)^2-sqrt{10*607741-(2217)^2}}

$$r = \frac { 10 * 535134 - 2217 * 2489 } { \sqrt { 10 * 695135 - ( 2489 ) ^ { 2 } } - \sqrt { 10 * 607741 - ( 2217 ) ^ { 2 } } }$$

Whakaoti mō r

$$r = \frac{55591 {(\sqrt{756229} + \sqrt{1162321})}}{135364} \approx 799.887238416$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Whakareatia te 10 ki te 535134, ka 5351340.

$$r=\frac{5351340-2217\times 2489}{\sqrt{10\times 695135-2489^{2}}-\sqrt{10\times 607741-2217^{2}}}$$

Whakareatia te 2217 ki te 2489, ka 5518113.

$$r=\frac{5351340-5518113}{\sqrt{10\times 695135-2489^{2}}-\sqrt{10\times 607741-2217^{2}}}$$

Tangohia te 5518113 i te 5351340, ka -166773.

$$r=\frac{-166773}{\sqrt{10\times 695135-2489^{2}}-\sqrt{10\times 607741-2217^{2}}}$$

Whakareatia te 10 ki te 695135, ka 6951350.

$$r=\frac{-166773}{\sqrt{6951350-2489^{2}}-\sqrt{10\times 607741-2217^{2}}}$$

Tātaihia te 2489 mā te pū o 2, kia riro ko 6195121.

$$r=\frac{-166773}{\sqrt{6951350-6195121}-\sqrt{10\times 607741-2217^{2}}}$$

Tangohia te 6195121 i te 6951350, ka 756229.

$$r=\frac{-166773}{\sqrt{756229}-\sqrt{10\times 607741-2217^{2}}}$$

Whakareatia te 10 ki te 607741, ka 6077410.

$$r=\frac{-166773}{\sqrt{756229}-\sqrt{6077410-2217^{2}}}$$

Tātaihia te 2217 mā te pū o 2, kia riro ko 4915089.

$$r=\frac{-166773}{\sqrt{756229}-\sqrt{6077410-4915089}}$$

Tangohia te 4915089 i te 6077410, ka 1162321.

$$r=\frac{-166773}{\sqrt{756229}-\sqrt{1162321}}$$

Whakangāwaritia te tauraro o \frac{-166773}{\sqrt{756229}-\sqrt{1162321}} mā te whakarea i te taurunga me te tauraro ki te \sqrt{756229}+\sqrt{1162321}.

$$r=\frac{-166773\left(\sqrt{756229}+\sqrt{1162321}\right)}{\left(\sqrt{756229}-\sqrt{1162321}\right)\left(\sqrt{756229}+\sqrt{1162321}\right)}$$

Whakaarohia te \left(\sqrt{756229}-\sqrt{1162321}\right)\left(\sqrt{756229}+\sqrt{1162321}\right). Ka taea te whakareanga te panoni ki te rerekētanga o ngā pūrua mā te ture: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$r=\frac{-166773\left(\sqrt{756229}+\sqrt{1162321}\right)}{\left(\sqrt{756229}\right)^{2}-\left(\sqrt{1162321}\right)^{2}}$$

Pūrua \sqrt{756229}. Pūrua \sqrt{1162321}.

$$r=\frac{-166773\left(\sqrt{756229}+\sqrt{1162321}\right)}{756229-1162321}$$

Tangohia te 1162321 i te 756229, ka -406092.

$$r=\frac{-166773\left(\sqrt{756229}+\sqrt{1162321}\right)}{-406092}$$

Whakawehea te -166773\left(\sqrt{756229}+\sqrt{1162321}\right) ki te -406092, kia riro ko \frac{55591}{135364}\left(\sqrt{756229}+\sqrt{1162321}\right).

$$r=\frac{55591}{135364}\left(\sqrt{756229}+\sqrt{1162321}\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te \frac{55591}{135364} ki te \sqrt{756229}+\sqrt{1162321}.

$$r=\frac{55591}{135364}\sqrt{756229}+\frac{55591}{135364}\sqrt{1162321}$$

Tautapa r

$$r≔\frac{55591\left(\sqrt{756229}+\sqrt{1162321}\right)}{135364}$$