Solve sqrt{45div1/5*8/3}*2

$$\sqrt{ 45 \div \frac{ 1 }{ 5 } \times \frac{ 8 }{ 3 } } \times 2$$

Evaluate

$$20\sqrt{6}\approx 48.989794856$$

Solution Steps

Divide 45 by \frac{1}{5} by multiplying 45 by the reciprocal of \frac{1}{5}.

$$2\sqrt{45\times 5\times \frac{8}{3}}$$

Multiply 45 and 5 to get 225.

$$2\sqrt{225\times \frac{8}{3}}$$

Express 225\times \frac{8}{3} as a single fraction.

$$2\sqrt{\frac{225\times 8}{3}}$$

Multiply 225 and 8 to get 1800.

$$2\sqrt{\frac{1800}{3}}$$

Divide 1800 by 3 to get 600.

$$2\sqrt{600}$$

Factor 600=10^{2}\times 6. Rewrite the square root of the product \sqrt{10^{2}\times 6} as the product of square roots \sqrt{10^{2}}\sqrt{6}. Take the square root of 10^{2}.

$$2\times 10\sqrt{6}$$

Multiply 2 and 10 to get 20.

$$20\sqrt{6}$$