Solve sqrt{4^2-{left(16/5right)}^2}

$$\sqrt{ { 4 }^{ 2 } - { \left( \frac{ 16 }{ 5 } \right) }^{ 2 } }$$

Evaluate

$$\frac{12}{5}=2.4$$

Solution Steps

Calculate 4 to the power of 2 and get 16.

$$\sqrt{16-\left(\frac{16}{5}\right)^{2}}$$

Calculate \frac{16}{5} to the power of 2 and get \frac{256}{25}.

$$\sqrt{16-\frac{256}{25}}$$

Convert 16 to fraction \frac{400}{25}.

$$\sqrt{\frac{400}{25}-\frac{256}{25}}$$

Since \frac{400}{25} and \frac{256}{25} have the same denominator, subtract them by subtracting their numerators.

$$\sqrt{\frac{400-256}{25}}$$

Subtract 256 from 400 to get 144.

$$\sqrt{\frac{144}{25}}$$

Rewrite the square root of the division \frac{144}{25} as the division of square roots \frac{\sqrt{144}}{\sqrt{25}}. Take the square root of both numerator and denominator.

$$\frac{12}{5}$$

Factor

$$\frac{2 ^ {2} \cdot 3}{5} = 2\frac{2}{5} = 2.4$$