Solve 0.63sqrt{24}*(250)(500)^2/6

$$0.63 \sqrt { 24 } \times \frac { ( 250 ) ( 500 ) ^ { 2 } } { 6 }$$

Evaluate

$$13125000\sqrt{6}\approx 32149552.874029208$$

Solution Steps

Factor 24=2^{2}\times 6. Rewrite the square root of the product \sqrt{2^{2}\times 6} as the product of square roots \sqrt{2^{2}}\sqrt{6}. Take the square root of 2^{2}.

$$0.63\times 2\sqrt{6}\times \frac{250\times 500^{2}}{6}$$

Multiply 0.63 and 2 to get 1.26.

$$1.26\sqrt{6}\times \frac{250\times 500^{2}}{6}$$

Calculate 500 to the power of 2 and get 250000.

$$1.26\sqrt{6}\times \frac{250\times 250000}{6}$$

Multiply 250 and 250000 to get 62500000.

$$1.26\sqrt{6}\times \frac{62500000}{6}$$

Reduce the fraction \frac{62500000}{6} to lowest terms by extracting and canceling out 2.

$$1.26\sqrt{6}\times \frac{31250000}{3}$$

Convert decimal number 1.26 to fraction \frac{126}{100}. Reduce the fraction \frac{126}{100} to lowest terms by extracting and canceling out 2.

$$\frac{63}{50}\sqrt{6}\times \frac{31250000}{3}$$

Multiply \frac{63}{50} times \frac{31250000}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{63\times 31250000}{50\times 3}\sqrt{6}$$

Do the multiplications in the fraction \frac{63\times 31250000}{50\times 3}.

$$\frac{1968750000}{150}\sqrt{6}$$

Divide 1968750000 by 150 to get 13125000.

$$13125000\sqrt{6}$$