Solve sqrt{31/16*234/81}

$$\sqrt { 3 \frac { 1 } { 16 } \times 2 \frac { 34 } { 81 } }$$

Evaluate

$$\frac{49}{18}\approx 2.722222222$$

Solution Steps

Multiply 3 and 16 to get 48.

$$\sqrt{\frac{48+1}{16}\times \frac{2\times 81+34}{81}}$$

Add 48 and 1 to get 49.

$$\sqrt{\frac{49}{16}\times \frac{2\times 81+34}{81}}$$

Multiply 2 and 81 to get 162.

$$\sqrt{\frac{49}{16}\times \frac{162+34}{81}}$$

Add 162 and 34 to get 196.

$$\sqrt{\frac{49}{16}\times \frac{196}{81}}$$

Multiply \frac{49}{16} times \frac{196}{81} by multiplying numerator times numerator and denominator times denominator.

$$\sqrt{\frac{49\times 196}{16\times 81}}$$

Do the multiplications in the fraction \frac{49\times 196}{16\times 81}.

$$\sqrt{\frac{9604}{1296}}$$

Reduce the fraction \frac{9604}{1296} to lowest terms by extracting and canceling out 4.

$$\sqrt{\frac{2401}{324}}$$

Rewrite the square root of the division \frac{2401}{324} as the division of square roots \frac{\sqrt{2401}}{\sqrt{324}}. Take the square root of both numerator and denominator.

$$\frac{49}{18}$$

Factor

$$\frac{7 ^ {2}}{2 \cdot 3 ^ {2}} = 2\frac{13}{18} = 2.7222222222222223$$