Solve sqrt{20}:10^-1-50/sqrt{5}+sqrt{500}-4^-1*sqrt{2880}

$$\sqrt { 20 } : 10 ^ { - 1 } - \frac { 50 } { \sqrt { 5 } } + \sqrt { 500 } - 4 ^ { - 1 } \cdot \sqrt { 2880 }$$

Evaluate

$$14\sqrt{5}\approx 31.304951685$$

Solution Steps

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}.

$$\frac{2\sqrt{5}}{10^{-1}}-\frac{50}{\sqrt{5}}+\sqrt{500}-4^{-1}\sqrt{2880}$$

Calculate 10 to the power of -1 and get \frac{1}{10}.

$$\frac{2\sqrt{5}}{\frac{1}{10}}-\frac{50}{\sqrt{5}}+\sqrt{500}-4^{-1}\sqrt{2880}$$

Divide 2\sqrt{5} by \frac{1}{10} by multiplying 2\sqrt{5} by the reciprocal of \frac{1}{10}.

$$2\sqrt{5}\times 10-\frac{50}{\sqrt{5}}+\sqrt{500}-4^{-1}\sqrt{2880}$$

Multiply 2 and 10 to get 20.

$$20\sqrt{5}-\frac{50}{\sqrt{5}}+\sqrt{500}-4^{-1}\sqrt{2880}$$

Rationalize the denominator of \frac{50}{\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.

$$20\sqrt{5}-\frac{50\sqrt{5}}{\left(\sqrt{5}\right)^{2}}+\sqrt{500}-4^{-1}\sqrt{2880}$$

The square of \sqrt{5} is 5.

$$20\sqrt{5}-\frac{50\sqrt{5}}{5}+\sqrt{500}-4^{-1}\sqrt{2880}$$

Divide 50\sqrt{5} by 5 to get 10\sqrt{5}.

$$20\sqrt{5}-10\sqrt{5}+\sqrt{500}-4^{-1}\sqrt{2880}$$

Factor 500=10^{2}\times 5. Rewrite the square root of the product \sqrt{10^{2}\times 5} as the product of square roots \sqrt{10^{2}}\sqrt{5}. Take the square root of 10^{2}.

$$20\sqrt{5}-10\sqrt{5}+10\sqrt{5}-4^{-1}\sqrt{2880}$$

Combine 20\sqrt{5} and 10\sqrt{5} to get 30\sqrt{5}.

$$30\sqrt{5}-10\sqrt{5}-4^{-1}\sqrt{2880}$$

Calculate 4 to the power of -1 and get \frac{1}{4}.

$$30\sqrt{5}-10\sqrt{5}-\frac{1}{4}\sqrt{2880}$$

Factor 2880=24^{2}\times 5. Rewrite the square root of the product \sqrt{24^{2}\times 5} as the product of square roots \sqrt{24^{2}}\sqrt{5}. Take the square root of 24^{2}.

$$30\sqrt{5}-10\sqrt{5}-\frac{1}{4}\times 24\sqrt{5}$$

Multiply \frac{1}{4} and 24 to get 6.

$$30\sqrt{5}-10\sqrt{5}-6\sqrt{5}$$

Combine 30\sqrt{5} and -6\sqrt{5} to get 24\sqrt{5}.

$$24\sqrt{5}-10\sqrt{5}$$

Combine 24\sqrt{5} and -10\sqrt{5} to get 14\sqrt{5}.

$$14\sqrt{5}$$