Solve sqrt{36}-sqrt{(-3/2)^2}divsqrt{0.09}-(-sqrt{3})^2

$$\sqrt { 36 } - \sqrt { ( - \frac { 3 } { 2 } ) ^ { 2 } } \div \sqrt { 0.09 } - ( - \sqrt { 3 } ) ^ { 2 }$$

Evaluate

$$-2$$

Solution Steps

Calculate the square root of 36 and get 6.

$$6-\frac{\sqrt{\left(-\frac{3}{2}\right)^{2}}}{\sqrt{0.09}}-\left(-\sqrt{3}\right)^{2}$$

Calculate -\frac{3}{2} to the power of 2 and get \frac{9}{4}.

$$6-\frac{\sqrt{\frac{9}{4}}}{\sqrt{0.09}}-\left(-\sqrt{3}\right)^{2}$$

Rewrite the square root of the division \frac{9}{4} as the division of square roots \frac{\sqrt{9}}{\sqrt{4}}. Take the square root of both numerator and denominator.

$$6-\frac{\frac{3}{2}}{\sqrt{0.09}}-\left(-\sqrt{3}\right)^{2}$$

Calculate the square root of 0.09 and get 0.3.

$$6-\frac{\frac{3}{2}}{0.3}-\left(-\sqrt{3}\right)^{2}$$

Express \frac{\frac{3}{2}}{0.3} as a single fraction.

$$6-\frac{3}{2\times 0.3}-\left(-\sqrt{3}\right)^{2}$$

Multiply 2 and 0.3 to get 0.6.

$$6-\frac{3}{0.6}-\left(-\sqrt{3}\right)^{2}$$

Expand \frac{3}{0.6} by multiplying both numerator and the denominator by 10.

$$6-\frac{30}{6}-\left(-\sqrt{3}\right)^{2}$$

Divide 30 by 6 to get 5.

$$6-5-\left(-\sqrt{3}\right)^{2}$$

Subtract 5 from 6 to get 1.

$$1-\left(-\sqrt{3}\right)^{2}$$

Calculate -\sqrt{3} to the power of 2 and get \left(\sqrt{3}\right)^{2}.

$$1-\left(\sqrt{3}\right)^{2}$$

The square of \sqrt{3} is 3.

$$1-3$$

Subtract 3 from 1 to get -2.

$$-2$$

Factor

$$-2$$