Solve sqrt{51/16}*134/81

$$\sqrt{ 5 \frac{ 1 }{ 16 } } \times 1 \frac{ 34 }{ 81 }$$

Evaluate

$$\frac{115}{36}\approx 3.194444444$$

Solution Steps

Multiply 5 and 16 to get 80.

$$\sqrt{\frac{80+1}{16}}\times \frac{1\times 81+34}{81}$$

Add 80 and 1 to get 81.

$$\sqrt{\frac{81}{16}}\times \frac{1\times 81+34}{81}$$

Rewrite the square root of the division \frac{81}{16} as the division of square roots \frac{\sqrt{81}}{\sqrt{16}}. Take the square root of both numerator and denominator.

$$\frac{9}{4}\times \frac{1\times 81+34}{81}$$

Multiply 1 and 81 to get 81.

$$\frac{9}{4}\times \frac{81+34}{81}$$

Add 81 and 34 to get 115.

$$\frac{9}{4}\times \frac{115}{81}$$

Multiply \frac{9}{4} times \frac{115}{81} by multiplying numerator times numerator and denominator times denominator.

$$\frac{9\times 115}{4\times 81}$$

Do the multiplications in the fraction \frac{9\times 115}{4\times 81}.

$$\frac{1035}{324}$$

Reduce the fraction \frac{1035}{324} to lowest terms by extracting and canceling out 9.

$$\frac{115}{36}$$

Factor

$$\frac{5 \cdot 23}{2 ^ {2} \cdot 3 ^ {2}} = 3\frac{7}{36} = 3.1944444444444446$$