Solve frac{595sqrt{41}}{492}*164/215sqrt{41}

$$\frac{ 595 \sqrt{ 41 } }{ 492 } \times \frac{ 164 }{ 215 \sqrt{ 41 } }$$

Evaluate

$$\frac{119}{129}\approx 0.92248062$$

Solution Steps

Rationalize the denominator of \frac{164}{215\sqrt{41}} by multiplying numerator and denominator by \sqrt{41}.

$$\frac{595\sqrt{41}}{492}\times \frac{164\sqrt{41}}{215\left(\sqrt{41}\right)^{2}}$$

The square of \sqrt{41} is 41.

$$\frac{595\sqrt{41}}{492}\times \frac{164\sqrt{41}}{215\times 41}$$

Cancel out 41 in both numerator and denominator.

$$\frac{595\sqrt{41}}{492}\times \frac{4\sqrt{41}}{215}$$

Multiply \frac{595\sqrt{41}}{492} times \frac{4\sqrt{41}}{215} by multiplying numerator times numerator and denominator times denominator.

$$\frac{595\sqrt{41}\times 4\sqrt{41}}{492\times 215}$$

Cancel out 4\times 5 in both numerator and denominator.

$$\frac{119\sqrt{41}\sqrt{41}}{43\times 123}$$

Multiply \sqrt{41} and \sqrt{41} to get 41.

$$\frac{119\times 41}{43\times 123}$$

Cancel out 41 in both numerator and denominator.

$$\frac{119}{3\times 43}$$

Multiply 3 and 43 to get 129.

$$\frac{119}{129}$$

Factor

$$\frac{7 \cdot 17}{3 \cdot 43} = 0.9224806201550387$$