Solve 4sqrt{(120)(140)(100)(120)}

$$4 \sqrt{ (120)(140)(100)(120) }$$

Evaluate

$$9600\sqrt{35}\approx 56794.365917756$$

Solution Steps

Multiply 120 and 140 to get 16800.

$$4\sqrt{16800\times 100\times 120}$$

Multiply 16800 and 100 to get 1680000.

$$4\sqrt{1680000\times 120}$$

Multiply 1680000 and 120 to get 201600000.

$$4\sqrt{201600000}$$

Factor 201600000=2400^{2}\times 35. Rewrite the square root of the product \sqrt{2400^{2}\times 35} as the product of square roots \sqrt{2400^{2}}\sqrt{35}. Take the square root of 2400^{2}.

$$4\times 2400\sqrt{35}$$

Multiply 4 and 2400 to get 9600.

$$9600\sqrt{35}$$