Solve 1/3sqrt{081}-2sqrt{61/4}+1/10sqrt{64+36}

$$\frac { 1 } { 3 } \sqrt { 081 } - 2 \sqrt { 6 \frac { 1 } { 4 } } + \frac { 1 } { 10 } \sqrt { 64 + 36 }$$

Evaluate

$$-4$$

Solution Steps

Multiply 0 and 81 to get 0.

$$\frac{1}{3}\sqrt{0}-2\sqrt{\frac{6\times 4+1}{4}}+\frac{1}{10}\sqrt{64+36}$$

Calculate the square root of 0 and get 0.

$$\frac{1}{3}\times 0-2\sqrt{\frac{6\times 4+1}{4}}+\frac{1}{10}\sqrt{64+36}$$

Multiply \frac{1}{3} and 0 to get 0.

$$0-2\sqrt{\frac{6\times 4+1}{4}}+\frac{1}{10}\sqrt{64+36}$$

Multiply 6 and 4 to get 24.

$$0-2\sqrt{\frac{24+1}{4}}+\frac{1}{10}\sqrt{64+36}$$

Add 24 and 1 to get 25.

$$0-2\sqrt{\frac{25}{4}}+\frac{1}{10}\sqrt{64+36}$$

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.

$$0-2\times \frac{5}{2}+\frac{1}{10}\sqrt{64+36}$$

Cancel out 2 and 2.

$$0-5+\frac{1}{10}\sqrt{64+36}$$

Subtract 5 from 0 to get -5.

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

Add 64 and 36 to get 100.

$$-5+\frac{1}{10}\sqrt{100}$$

Calculate the square root of 100 and get 10.

$$-5+\frac{1}{10}\times 10$$

Cancel out 10 and 10.

$$-5+1$$

Add -5 and 1 to get -4.

$$-4$$

Factor

$$-4$$