Solve frac{(8^2-4(8)+4)sqrt{8}}{27}-(5^2-45)+45/27

$$\frac { ( 8 ^ { 2 } - 4 ( 8 ) + 4 ) \sqrt { 8 } } { 27 } - \frac { ( 5 ^ { 2 } - 45 ) + 45 } { 27 }$$

Evaluate

$$\frac{8\sqrt{2}}{3}-\frac{25}{27}\approx 2.84531024$$

Solution Steps

Calculate 8 to the power of 2 and get 64.

$$\frac{\left(64-4\times 8+4\right)\sqrt{8}}{27}-\frac{5^{2}-45+45}{27}$$

Multiply 4 and 8 to get 32.

$$\frac{\left(64-32+4\right)\sqrt{8}}{27}-\frac{5^{2}-45+45}{27}$$

Subtract 32 from 64 to get 32.

$$\frac{\left(32+4\right)\sqrt{8}}{27}-\frac{5^{2}-45+45}{27}$$

Add 32 and 4 to get 36.

$$\frac{36\sqrt{8}}{27}-\frac{5^{2}-45+45}{27}$$

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}.

$$\frac{36\times 2\sqrt{2}}{27}-\frac{5^{2}-45+45}{27}$$

Multiply 36 and 2 to get 72.

$$\frac{72\sqrt{2}}{27}-\frac{5^{2}-45+45}{27}$$

Divide 72\sqrt{2} by 27 to get \frac{8}{3}\sqrt{2}.

$$\frac{8}{3}\sqrt{2}-\frac{5^{2}-45+45}{27}$$

Calculate 5 to the power of 2 and get 25.

$$\frac{8}{3}\sqrt{2}-\frac{25-45+45}{27}$$

Subtract 45 from 25 to get -20.

$$\frac{8}{3}\sqrt{2}-\frac{-20+45}{27}$$

Add -20 and 45 to get 25.

$$\frac{8}{3}\sqrt{2}-\frac{25}{27}$$

Factor

$$\frac{72 \sqrt{2} - 25}{27} = 2.845310240402328$$