Solve (2.2*2.2*1-1/3*1*(2.2^2+sqrt{2.2^2*0.75^2}+0.75^2))*2

$$(2.2 \times 2.2 \times 1- \frac{ 1 }{ 3 } \times 1 \times ( { 2.2 }^{ 2 } + \sqrt{ { 2.2 }^{ 2 } \times { 0.75 }^{ 2 } } + { 0.75 }^{ 2 } )) \times 2$$

Evaluate

$$\frac{2987}{600}\approx 4.978333333$$

Solution Steps

Multiply 2.2 and 2.2 to get 4.84.

$$2\left(4.84\times 1-1\times \frac{1}{3}\left(2.2^{2}+\sqrt{2.2^{2}\times 0.75^{2}}+0.75^{2}\right)\right)$$

Multiply 4.84 and 1 to get 4.84.

$$2\left(4.84-1\times \frac{1}{3}\left(2.2^{2}+\sqrt{2.2^{2}\times 0.75^{2}}+0.75^{2}\right)\right)$$

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

$$2\left(4.84-\frac{1}{3}\left(2.2^{2}+\sqrt{2.2^{2}\times 0.75^{2}}+0.75^{2}\right)\right)$$

Calculate 2.2 to the power of 2 and get 4.84.

$$2\left(4.84-\frac{1}{3}\left(4.84+\sqrt{2.2^{2}\times 0.75^{2}}+0.75^{2}\right)\right)$$

Calculate 2.2 to the power of 2 and get 4.84.

$$2\left(4.84-\frac{1}{3}\left(4.84+\sqrt{4.84\times 0.75^{2}}+0.75^{2}\right)\right)$$

Calculate 0.75 to the power of 2 and get 0.5625.

$$2\left(4.84-\frac{1}{3}\left(4.84+\sqrt{4.84\times 0.5625}+0.75^{2}\right)\right)$$

Multiply 4.84 and 0.5625 to get 2.7225.

$$2\left(4.84-\frac{1}{3}\left(4.84+\sqrt{2.7225}+0.75^{2}\right)\right)$$

Calculate the square root of 2.7225 and get 1.65.

$$2\left(4.84-\frac{1}{3}\left(4.84+1.65+0.75^{2}\right)\right)$$

Add 4.84 and 1.65 to get 6.49.

$$2\left(4.84-\frac{1}{3}\left(6.49+0.75^{2}\right)\right)$$

Calculate 0.75 to the power of 2 and get 0.5625.

$$2\left(4.84-\frac{1}{3}\left(6.49+0.5625\right)\right)$$

Add 6.49 and 0.5625 to get 7.0525.

$$2\left(4.84-\frac{1}{3}\times 7.0525\right)$$

Convert decimal number 7.0525 to fraction \frac{70525}{10000}. Reduce the fraction \frac{70525}{10000} to lowest terms by extracting and canceling out 25.

$$2\left(4.84-\frac{1}{3}\times \frac{2821}{400}\right)$$

Multiply \frac{1}{3} times \frac{2821}{400} by multiplying numerator times numerator and denominator times denominator.

$$2\left(4.84-\frac{1\times 2821}{3\times 400}\right)$$

Do the multiplications in the fraction \frac{1\times 2821}{3\times 400}.

$$2\left(4.84-\frac{2821}{1200}\right)$$

Convert decimal number 4.84 to fraction \frac{484}{100}. Reduce the fraction \frac{484}{100} to lowest terms by extracting and canceling out 4.

$$2\left(\frac{121}{25}-\frac{2821}{1200}\right)$$

Least common multiple of 25 and 1200 is 1200. Convert \frac{121}{25} and \frac{2821}{1200} to fractions with denominator 1200.

$$2\left(\frac{5808}{1200}-\frac{2821}{1200}\right)$$

Since \frac{5808}{1200} and \frac{2821}{1200} have the same denominator, subtract them by subtracting their numerators.

$$2\times \frac{5808-2821}{1200}$$

Subtract 2821 from 5808 to get 2987.

$$2\times \frac{2987}{1200}$$

Express 2\times \frac{2987}{1200} as a single fraction.

$$\frac{2\times 2987}{1200}$$

Multiply 2 and 2987 to get 5974.

$$\frac{5974}{1200}$$

Reduce the fraction \frac{5974}{1200} to lowest terms by extracting and canceling out 2.

$$\frac{2987}{600}$$

Factor

$$\frac{29 \cdot 103}{3 \cdot 2 ^ {3} \cdot 5 ^ {2}} = 4\frac{587}{600} = 4.9783333333333335$$