Solve sqrt{(-0.5)^2}*(-sqrt{8})^2-sqrt{9}divsqrt{(3/4)^2}

$$\sqrt { ( - 0.5 ) ^ { 2 } } \times ( - \sqrt { 8 } ) ^ { 2 } - \sqrt { 9 } \div \sqrt { ( \frac { 3 } { 4 } ) ^ { 2 } }$$

Evaluate

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Solution Steps

Calculate -0.5 to the power of 2 and get 0.25.

$$\sqrt{0.25}\left(-\sqrt{8}\right)^{2}-\frac{\sqrt{9}}{\sqrt{\left(\frac{3}{4}\right)^{2}}}$$

Calculate the square root of 0.25 and get 0.5.

$$0.5\left(-\sqrt{8}\right)^{2}-\frac{\sqrt{9}}{\sqrt{\left(\frac{3}{4}\right)^{2}}}$$

Factor 8=2^{2}\times 2. Rewrite the square root of the product \sqrt{2^{2}\times 2} as the product of square roots \sqrt{2^{2}}\sqrt{2}. Take the square root of 2^{2}.

$$0.5\left(-2\sqrt{2}\right)^{2}-\frac{\sqrt{9}}{\sqrt{\left(\frac{3}{4}\right)^{2}}}$$

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

$$0.5\times \left(2\sqrt{2}\right)^{2}-\frac{\sqrt{9}}{\sqrt{\left(\frac{3}{4}\right)^{2}}}$$

Expand \left(2\sqrt{2}\right)^{2}.

$$0.5\times 2^{2}\left(\sqrt{2}\right)^{2}-\frac{\sqrt{9}}{\sqrt{\left(\frac{3}{4}\right)^{2}}}$$

Calculate 2 to the power of 2 and get 4.

$$0.5\times 4\left(\sqrt{2}\right)^{2}-\frac{\sqrt{9}}{\sqrt{\left(\frac{3}{4}\right)^{2}}}$$

The square of \sqrt{2} is 2.

$$0.5\times 4\times 2-\frac{\sqrt{9}}{\sqrt{\left(\frac{3}{4}\right)^{2}}}$$

Multiply 4 and 2 to get 8.

$$0.5\times 8-\frac{\sqrt{9}}{\sqrt{\left(\frac{3}{4}\right)^{2}}}$$

Multiply 0.5 and 8 to get 4.

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

Calculate the square root of 9 and get 3.

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

Calculate \frac{3}{4} to the power of 2 and get \frac{9}{16}.

$$4-\frac{3}{\sqrt{\frac{9}{16}}}$$

Rewrite the square root of the division \frac{9}{16} as the division of square roots \frac{\sqrt{9}}{\sqrt{16}}. Take the square root of both numerator and denominator.

$$4-\frac{3}{\frac{3}{4}}$$

Divide 3 by \frac{3}{4} by multiplying 3 by the reciprocal of \frac{3}{4}.

$$4-3\times \frac{4}{3}$$

Multiply 3 and \frac{4}{3} to get 4.

$$4-4$$

Subtract 4 from 4 to get 0.

$$0$$

Factor

$$0$$