Solve sqrt{4^2+(8/3)^2-2*4*8/3*9/16}

$$\sqrt { 4 ^ { 2 } + ( \frac { 8 } { 3 } ) ^ { 2 } - 2 \times 4 \times \frac { 8 } { 3 } \times \frac { 9 } { 16 } }$$

Evaluate

$$\frac{10}{3}\approx 3.333333333$$

Solution Steps

Calculate 4 to the power of 2 and get 16.

$$\sqrt{16+\left(\frac{8}{3}\right)^{2}-2\times 4\times \frac{8}{3}\times \frac{9}{16}}$$

Calculate \frac{8}{3} to the power of 2 and get \frac{64}{9}.

$$\sqrt{16+\frac{64}{9}-2\times 4\times \frac{8}{3}\times \frac{9}{16}}$$

Convert 16 to fraction \frac{144}{9}.

$$\sqrt{\frac{144}{9}+\frac{64}{9}-2\times 4\times \frac{8}{3}\times \frac{9}{16}}$$

Since \frac{144}{9} and \frac{64}{9} have the same denominator, add them by adding their numerators.

$$\sqrt{\frac{144+64}{9}-2\times 4\times \frac{8}{3}\times \frac{9}{16}}$$

Add 144 and 64 to get 208.

$$\sqrt{\frac{208}{9}-2\times 4\times \frac{8}{3}\times \frac{9}{16}}$$

Multiply 2 and 4 to get 8.

$$\sqrt{\frac{208}{9}-8\times \frac{8}{3}\times \frac{9}{16}}$$

Express 8\times \frac{8}{3} as a single fraction.

$$\sqrt{\frac{208}{9}-\frac{8\times 8}{3}\times \frac{9}{16}}$$

Multiply 8 and 8 to get 64.

$$\sqrt{\frac{208}{9}-\frac{64}{3}\times \frac{9}{16}}$$

Multiply \frac{64}{3} times \frac{9}{16} by multiplying numerator times numerator and denominator times denominator.

$$\sqrt{\frac{208}{9}-\frac{64\times 9}{3\times 16}}$$

Do the multiplications in the fraction \frac{64\times 9}{3\times 16}.

$$\sqrt{\frac{208}{9}-\frac{576}{48}}$$

Divide 576 by 48 to get 12.

$$\sqrt{\frac{208}{9}-12}$$

Convert 12 to fraction \frac{108}{9}.

$$\sqrt{\frac{208}{9}-\frac{108}{9}}$$

Since \frac{208}{9} and \frac{108}{9} have the same denominator, subtract them by subtracting their numerators.

$$\sqrt{\frac{208-108}{9}}$$

Subtract 108 from 208 to get 100.

$$\sqrt{\frac{100}{9}}$$

Rewrite the square root of the division \frac{100}{9} as the division of square roots \frac{\sqrt{100}}{\sqrt{9}}. Take the square root of both numerator and denominator.

$$\frac{10}{3}$$

Factor

$$\frac{2 \cdot 5}{3} = 3\frac{1}{3} = 3.3333333333333335$$