Solve sqrt{[9(3474684)-(5372)^2][9(16,060)-(366)^2]}

$$\sqrt { [ 9 ( 3474684 ) - ( 5372 ) ^ { 2 } ] [ 9 ( 16,060 ) - ( 366 ) ^ { 2 } ] }$$

Evaluate

$$84\sqrt{3620658}\approx 159835.424258829$$

Solution Steps

Multiply 9 and 3474684 to get 31272156.

$$\sqrt{\left(31272156-5372^{2}\right)\left(9\times 16060-366^{2}\right)}$$

Calculate 5372 to the power of 2 and get 28858384.

$$\sqrt{\left(31272156-28858384\right)\left(9\times 16060-366^{2}\right)}$$

Subtract 28858384 from 31272156 to get 2413772.

$$\sqrt{2413772\left(9\times 16060-366^{2}\right)}$$

Multiply 9 and 16060 to get 144540.

$$\sqrt{2413772\left(144540-366^{2}\right)}$$

Calculate 366 to the power of 2 and get 133956.

$$\sqrt{2413772\left(144540-133956\right)}$$

Subtract 133956 from 144540 to get 10584.

$$\sqrt{2413772\times 10584}$$

Multiply 2413772 and 10584 to get 25547362848.

$$\sqrt{25547362848}$$

Factor 25547362848=84^{2}\times 3620658. Rewrite the square root of the product \sqrt{84^{2}\times 3620658} as the product of square roots \sqrt{84^{2}}\sqrt{3620658}. Take the square root of 84^{2}.

$$84\sqrt{3620658}$$