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

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

Solve for r

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

Steps for Solving Linear Equation

Multiply 10 and 535134 to get 5351340.

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

Multiply 2217 and 2489 to get 5518113.

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

Subtract 5518113 from 5351340 to get -166773.

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

Multiply 10 and 695135 to get 6951350.

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

Calculate 2489 to the power of 2 and get 6195121.

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

Subtract 6195121 from 6951350 to get 756229.

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

Multiply 10 and 607741 to get 6077410.

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

Calculate 2217 to the power of 2 and get 4915089.

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

Subtract 4915089 from 6077410 to get 1162321.

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

Rationalize the denominator of \frac{-166773}{\sqrt{756229}-\sqrt{1162321}} by multiplying numerator and denominator by \sqrt{756229}+\sqrt{1162321}.

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

Consider \left(\sqrt{756229}-\sqrt{1162321}\right)\left(\sqrt{756229}+\sqrt{1162321}\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

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

Square \sqrt{756229}. Square \sqrt{1162321}.

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

Subtract 1162321 from 756229 to get -406092.

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

Divide -166773\left(\sqrt{756229}+\sqrt{1162321}\right) by -406092 to get \frac{55591}{135364}\left(\sqrt{756229}+\sqrt{1162321}\right).

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

Use the distributive property to multiply \frac{55591}{135364} by \sqrt{756229}+\sqrt{1162321}.

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

Assign r

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