Solve sqrt{(-19/16)^2}

$$\sqrt { ( - 1 \frac { 9 } { 16 } ) ^ { 2 } }$$

Evaluate

$$\frac{25}{16}=1.5625$$

Solution Steps

Multiply 1 and 16 to get 16.

$$\sqrt{\left(-\frac{16+9}{16}\right)^{2}}$$

Add 16 and 9 to get 25.

$$\sqrt{\left(-\frac{25}{16}\right)^{2}}$$

Calculate -\frac{25}{16} to the power of 2 and get \frac{625}{256}.

$$\sqrt{\frac{625}{256}}$$

Rewrite the square root of the division \frac{625}{256} as the division of square roots \frac{\sqrt{625}}{\sqrt{256}}. Take the square root of both numerator and denominator.

$$\frac{25}{16}$$

Factor

$$\frac{5 ^ {2}}{2 ^ {4}} = 1\frac{9}{16} = 1.5625$$