Solve 4sqrt{121/4}-frac{sqrt{0.64}}{sqrt{0.16}}

$$4 \sqrt { 12 \frac { 1 } { 4 } } - \frac { \sqrt { 0.64 } } { \sqrt { 0.16 } }$$

Evaluate

$$12$$

Solution Steps

Multiply 12 and 4 to get 48.

$$4\sqrt{\frac{48+1}{4}}-\frac{\sqrt{0.64}}{\sqrt{0.16}}$$

Add 48 and 1 to get 49.

$$4\sqrt{\frac{49}{4}}-\frac{\sqrt{0.64}}{\sqrt{0.16}}$$

Rewrite the square root of the division \frac{49}{4} as the division of square roots \frac{\sqrt{49}}{\sqrt{4}}. Take the square root of both numerator and denominator.

$$4\times \frac{7}{2}-\frac{\sqrt{0.64}}{\sqrt{0.16}}$$

Express 4\times \frac{7}{2} as a single fraction.

$$\frac{4\times 7}{2}-\frac{\sqrt{0.64}}{\sqrt{0.16}}$$

Multiply 4 and 7 to get 28.

$$\frac{28}{2}-\frac{\sqrt{0.64}}{\sqrt{0.16}}$$

Divide 28 by 2 to get 14.

$$14-\frac{\sqrt{0.64}}{\sqrt{0.16}}$$

Calculate the square root of 0.64 and get 0.8.

$$14-\frac{0.8}{\sqrt{0.16}}$$

Calculate the square root of 0.16 and get 0.4.

$$14-\frac{0.8}{0.4}$$

Expand \frac{0.8}{0.4} by multiplying both numerator and the denominator by 10.

$$14-\frac{8}{4}$$

Divide 8 by 4 to get 2.

$$14-2$$

Subtract 2 from 14 to get 12.

$$12$$

Factor

$$3\times 2^{2}$$