Solve frac{(sqrt{164}-sqrt{41})*sqrt{61}}{2}

$$\frac{ ( \sqrt{ 164 } - \sqrt{ 41 } ) \times \sqrt{ 61 } }{ 2 }$$

Evaluate

$$\frac{\sqrt{2501}}{2}\approx 25.0049995$$

Solution Steps

Factor 164=2^{2}\times 41. Rewrite the square root of the product \sqrt{2^{2}\times 41} as the product of square roots \sqrt{2^{2}}\sqrt{41}. Take the square root of 2^{2}.

$$\frac{\left(2\sqrt{41}-\sqrt{41}\right)\sqrt{61}}{2}$$

Combine 2\sqrt{41} and -\sqrt{41} to get \sqrt{41}.

$$\frac{\sqrt{41}\sqrt{61}}{2}$$

To multiply \sqrt{41} and \sqrt{61}, multiply the numbers under the square root.

$$\frac{\sqrt{2501}}{2}$$