Solve sqrt{19/16}-sqrt{144}+sqrt{49}

$$\sqrt { 1 \frac { 9 } { 16 } } - \sqrt { 144 } + \sqrt { 49 }$$

Evaluate

$$-\frac{15}{4}=-3.75$$

Solution Steps

Multiply 1 and 16 to get 16.

$$\sqrt{\frac{16+9}{16}}-\sqrt{144}+\sqrt{49}$$

Add 16 and 9 to get 25.

$$\sqrt{\frac{25}{16}}-\sqrt{144}+\sqrt{49}$$

Rewrite the square root of the division \frac{25}{16} as the division of square roots \frac{\sqrt{25}}{\sqrt{16}}. Take the square root of both numerator and denominator.

$$\frac{5}{4}-\sqrt{144}+\sqrt{49}$$

Calculate the square root of 144 and get 12.

$$\frac{5}{4}-12+\sqrt{49}$$

Convert 12 to fraction \frac{48}{4}.

$$\frac{5}{4}-\frac{48}{4}+\sqrt{49}$$

Since \frac{5}{4} and \frac{48}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{5-48}{4}+\sqrt{49}$$

Subtract 48 from 5 to get -43.

$$-\frac{43}{4}+\sqrt{49}$$

Calculate the square root of 49 and get 7.

$$-\frac{43}{4}+7$$

Convert 7 to fraction \frac{28}{4}.

$$-\frac{43}{4}+\frac{28}{4}$$

Since -\frac{43}{4} and \frac{28}{4} have the same denominator, add them by adding their numerators.

$$\frac{-43+28}{4}$$

Add -43 and 28 to get -15.

$$-\frac{15}{4}$$

Factor

$$-\frac{15}{4} = -3\frac{3}{4} = -3.75$$