Solve frac{sqrt{144}}{sqrt{0.4}}-sqrt{2.56}sqrt{2500}

$$\frac{ \sqrt{ 144 } }{ \sqrt{ 0.4 } } - \sqrt{ 2.56 } \sqrt{ 2500 }$$

Evaluate

$$6\sqrt{10}-80\approx -61.026334039$$

Solution Steps

Rewrite the division of square roots \frac{\sqrt{144}}{\sqrt{0.4}} as the square root of the division \sqrt{\frac{144}{0.4}} and perform the division.

$$\sqrt{72}-\sqrt{2.56}\sqrt{2500}$$

Factor 72=6^{2}\times 2. Rewrite the square root of the product \sqrt{6^{2}\times 2} as the product of square roots \sqrt{6^{2}}\sqrt{2}. Take the square root of 6^{2}.

$$6\sqrt{2}-\sqrt{2.56}\sqrt{2500}$$

Calculate the square root of 2.56 and get 1.6.

$$6\sqrt{2}-1.6\sqrt{2500}$$

Calculate the square root of 2500 and get 50.

$$6\sqrt{2}-1.6\times 50$$

Multiply 1.6 and 50 to get 80.

$$6\sqrt{2}-80$$