Solve 2sqrt{20}1/4-sqrt{1}32/49

$$2 \sqrt{ 20 } \frac{ 1 }{ 4 } - \sqrt{ 1 } \frac{ 32 }{ 49 }$$

Evaluate

$$\sqrt{5}-\frac{32}{49}\approx 1.583006753$$

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}.

$$2\times 2\sqrt{5}\times \frac{1}{4}-\sqrt{1}\times \frac{32}{49}$$

Multiply 2 and 2 to get 4.

$$4\sqrt{5}\times \frac{1}{4}-\sqrt{1}\times \frac{32}{49}$$

Cancel out 4 and 4.

$$\sqrt{5}-\sqrt{1}\times \frac{32}{49}$$

Calculate the square root of 1 and get 1.

$$\sqrt{5}-1\times \frac{32}{49}$$

Multiply 1 and \frac{32}{49} to get \frac{32}{49}.

$$\sqrt{5}-\frac{32}{49}$$

Factor

$$\frac{49 \sqrt{5} - 32}{49} = 1.5830067530099938$$