Solve 0.0625^frac{1{4}}+[(-3)^4]^frac{1{4}}-(sqrt{5}-sqrt{3})^0+sqrt{33/8}

$$0.0625 ^ { \frac { 1 } { 4 } } + [ ( - 3 ) ^ { 4 } ] ^ { \frac { 1 } { 4 } } - ( \sqrt { 5 } - \sqrt { 3 } ) ^ { 0 } + \sqrt { 3 \frac { 3 } { 8 } }$$

Evaluate

$$\frac{3\sqrt{6}}{4}+2.5\approx 4.337117307$$

Short Solution Steps

To raise a power to another power, multiply the exponents. Multiply 4 and \frac{1}{4} to get 1.

$$0.0625^{\frac{1}{4}}+\left(-3\right)^{1}-\left(\sqrt{5}-\sqrt{3}\right)^{0}+\sqrt{\frac{3\times 8+3}{8}}$$

Calculate 0.0625 to the power of \frac{1}{4} and get \frac{1}{2}.

$$\frac{1}{2}+\left(-3\right)^{1}-\left(\sqrt{5}-\sqrt{3}\right)^{0}+\sqrt{\frac{3\times 8+3}{8}}$$

Calculate -3 to the power of 1 and get -3.

$$\frac{1}{2}-3-\left(\sqrt{5}-\sqrt{3}\right)^{0}+\sqrt{\frac{3\times 8+3}{8}}$$

Subtract 3 from \frac{1}{2} to get -\frac{5}{2}.

$$-\frac{5}{2}-\left(\sqrt{5}-\sqrt{3}\right)^{0}+\sqrt{\frac{3\times 8+3}{8}}$$

Calculate \sqrt{5}-\sqrt{3} to the power of 0 and get 1.

$$-\frac{5}{2}-1+\sqrt{\frac{3\times 8+3}{8}}$$

Subtract 1 from -\frac{5}{2} to get -\frac{7}{2}.

$$-\frac{7}{2}+\sqrt{\frac{3\times 8+3}{8}}$$

Multiply 3 and 8 to get 24.

$$-\frac{7}{2}+\sqrt{\frac{24+3}{8}}$$

Add 24 and 3 to get 27.

$$-\frac{7}{2}+\sqrt{\frac{27}{8}}$$

Rewrite the square root of the division \sqrt{\frac{27}{8}} as the division of square roots \frac{\sqrt{27}}{\sqrt{8}}.

$$-\frac{7}{2}+\frac{\sqrt{27}}{\sqrt{8}}$$

Factor 27=3^{2}\times 3. Rewrite the square root of the product \sqrt{3^{2}\times 3} as the product of square roots \sqrt{3^{2}}\sqrt{3}. Take the square root of 3^{2}.

$$-\frac{7}{2}+\frac{3\sqrt{3}}{\sqrt{8}}$$

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}.

$$-\frac{7}{2}+\frac{3\sqrt{3}}{2\sqrt{2}}$$

Rationalize the denominator of \frac{3\sqrt{3}}{2\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$-\frac{7}{2}+\frac{3\sqrt{3}\sqrt{2}}{2\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$-\frac{7}{2}+\frac{3\sqrt{3}\sqrt{2}}{2\times 2}$$

To multiply \sqrt{3} and \sqrt{2}, multiply the numbers under the square root.

$$-\frac{7}{2}+\frac{3\sqrt{6}}{2\times 2}$$

Multiply 2 and 2 to get 4.

$$-\frac{7}{2}+\frac{3\sqrt{6}}{4}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2 and 4 is 4. Multiply -\frac{7}{2} times \frac{2}{2}.

$$-\frac{7\times 2}{4}+\frac{3\sqrt{6}}{4}$$

Since -\frac{7\times 2}{4} and \frac{3\sqrt{6}}{4} have the same denominator, add them by adding their numerators.

$$\frac{-7\times 2+3\sqrt{6}}{4}$$

Do the multiplications in -7\times 2+3\sqrt{6}.

$$\frac{-14+3\sqrt{6}}{4}$$