Solve 1/3sqrt{0.81}-2sqrt{61/4}+1/10sqrt{64+36}

$$\frac { 1 } { 3 } \sqrt { 0.81 } - 2 \sqrt { 6 \frac { 1 } { 4 } } + \frac { 1 } { 10 } \sqrt { 64 + 36 }$$

Evaluate

$$-3.7$$

Solution Steps

Calculate the square root of 0.81 and get 0.9.

$$\frac{1}{3}\times 0.9-2\sqrt{\frac{6\times 4+1}{4}}+\frac{1}{10}\sqrt{64+36}$$

Convert decimal number 0.9 to fraction \frac{9}{10}.

$$\frac{1}{3}\times \frac{9}{10}-2\sqrt{\frac{6\times 4+1}{4}}+\frac{1}{10}\sqrt{64+36}$$

Multiply \frac{1}{3} times \frac{9}{10} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1\times 9}{3\times 10}-2\sqrt{\frac{6\times 4+1}{4}}+\frac{1}{10}\sqrt{64+36}$$

Do the multiplications in the fraction \frac{1\times 9}{3\times 10}.

$$\frac{9}{30}-2\sqrt{\frac{6\times 4+1}{4}}+\frac{1}{10}\sqrt{64+36}$$

Reduce the fraction \frac{9}{30} to lowest terms by extracting and canceling out 3.

$$\frac{3}{10}-2\sqrt{\frac{6\times 4+1}{4}}+\frac{1}{10}\sqrt{64+36}$$

Multiply 6 and 4 to get 24.

$$\frac{3}{10}-2\sqrt{\frac{24+1}{4}}+\frac{1}{10}\sqrt{64+36}$$

Add 24 and 1 to get 25.

$$\frac{3}{10}-2\sqrt{\frac{25}{4}}+\frac{1}{10}\sqrt{64+36}$$

Rewrite the square root of the division \frac{25}{4} as the division of square roots \frac{\sqrt{25}}{\sqrt{4}}. Take the square root of both numerator and denominator.

$$\frac{3}{10}-2\times \frac{5}{2}+\frac{1}{10}\sqrt{64+36}$$

Cancel out 2 and 2.

$$\frac{3}{10}-5+\frac{1}{10}\sqrt{64+36}$$

Convert 5 to fraction \frac{50}{10}.

$$\frac{3}{10}-\frac{50}{10}+\frac{1}{10}\sqrt{64+36}$$

Since \frac{3}{10} and \frac{50}{10} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3-50}{10}+\frac{1}{10}\sqrt{64+36}$$

Subtract 50 from 3 to get -47.

$$-\frac{47}{10}+\frac{1}{10}\sqrt{64+36}$$

Add 64 and 36 to get 100.

$$-\frac{47}{10}+\frac{1}{10}\sqrt{100}$$

Calculate the square root of 100 and get 10.

$$-\frac{47}{10}+\frac{1}{10}\times 10$$

Cancel out 10 and 10.

$$-\frac{47}{10}+1$$

Convert 1 to fraction \frac{10}{10}.

$$-\frac{47}{10}+\frac{10}{10}$$

Since -\frac{47}{10} and \frac{10}{10} have the same denominator, add them by adding their numerators.

$$\frac{-47+10}{10}$$

Add -47 and 10 to get -37.

$$-\frac{37}{10}$$

Factor

$$-3.7$$