Solve y=2(sqrt{360}+2sqrt{2}*sqrt{405})+3(sqrt{810}-sqrt{20}*sqrt{162})

$$y = 2 ( \sqrt { 360 } + 2 \sqrt { 2 } \cdot \sqrt { 405 } ) + 3 ( \sqrt { 810 } - \sqrt { 20 } \cdot \sqrt { 162 } )$$

Solve for y

$$y=21\sqrt{10}\approx 66.407830864$$

Steps for Solving Linear Equation

Factor 360=6^{2}\times 10. Rewrite the square root of the product \sqrt{6^{2}\times 10} as the product of square roots \sqrt{6^{2}}\sqrt{10}. Take the square root of 6^{2}.

$$y=2\left(6\sqrt{10}+2\sqrt{2}\sqrt{405}\right)+3\left(\sqrt{810}-\sqrt{20}\sqrt{162}\right)$$

Factor 405=9^{2}\times 5. Rewrite the square root of the product \sqrt{9^{2}\times 5} as the product of square roots \sqrt{9^{2}}\sqrt{5}. Take the square root of 9^{2}.

$$y=2\left(6\sqrt{10}+2\sqrt{2}\times 9\sqrt{5}\right)+3\left(\sqrt{810}-\sqrt{20}\sqrt{162}\right)$$

Multiply 2 and 9 to get 18.

$$y=2\left(6\sqrt{10}+18\sqrt{2}\sqrt{5}\right)+3\left(\sqrt{810}-\sqrt{20}\sqrt{162}\right)$$

To multiply \sqrt{2} and \sqrt{5}, multiply the numbers under the square root.

$$y=2\left(6\sqrt{10}+18\sqrt{10}\right)+3\left(\sqrt{810}-\sqrt{20}\sqrt{162}\right)$$

Combine 6\sqrt{10} and 18\sqrt{10} to get 24\sqrt{10}.

$$y=2\times 24\sqrt{10}+3\left(\sqrt{810}-\sqrt{20}\sqrt{162}\right)$$

Multiply 2 and 24 to get 48.

$$y=48\sqrt{10}+3\left(\sqrt{810}-\sqrt{20}\sqrt{162}\right)$$

Factor 810=9^{2}\times 10. Rewrite the square root of the product \sqrt{9^{2}\times 10} as the product of square roots \sqrt{9^{2}}\sqrt{10}. Take the square root of 9^{2}.

$$y=48\sqrt{10}+3\left(9\sqrt{10}-\sqrt{20}\sqrt{162}\right)$$

Factor 20=2^{2}\times 5. Rewrite the square root of the product \sqrt{2^{2}\times 5} as the product of square roots \sqrt{2^{2}}\sqrt{5}. Take the square root of 2^{2}.

$$y=48\sqrt{10}+3\left(9\sqrt{10}-2\sqrt{5}\sqrt{162}\right)$$

Factor 162=9^{2}\times 2. Rewrite the square root of the product \sqrt{9^{2}\times 2} as the product of square roots \sqrt{9^{2}}\sqrt{2}. Take the square root of 9^{2}.

$$y=48\sqrt{10}+3\left(9\sqrt{10}-2\sqrt{5}\times 9\sqrt{2}\right)$$

Multiply 2 and 9 to get 18.

$$y=48\sqrt{10}+3\left(9\sqrt{10}-18\sqrt{5}\sqrt{2}\right)$$

To multiply \sqrt{5} and \sqrt{2}, multiply the numbers under the square root.

$$y=48\sqrt{10}+3\left(9\sqrt{10}-18\sqrt{10}\right)$$

Combine 9\sqrt{10} and -18\sqrt{10} to get -9\sqrt{10}.

$$y=48\sqrt{10}+3\left(-9\right)\sqrt{10}$$

Multiply 3 and -9 to get -27.

$$y=48\sqrt{10}-27\sqrt{10}$$

Combine 48\sqrt{10} and -27\sqrt{10} to get 21\sqrt{10}.

$$y=21\sqrt{10}$$

Assign y

$$y≔21\sqrt{10}$$