Solve sqrt{16-4/9*-5^2}

$$\sqrt{ 16- \frac{ 4 }{ 9 } \times - { 5 }^{ 2 } }$$

Evaluate

$$\frac{2\sqrt{61}}{3}\approx 5.206833117$$

Solution Steps

Calculate 5 to the power of 2 and get 25.

$$\sqrt{16-\frac{4}{9}\left(-25\right)}$$

Express \frac{4}{9}\left(-25\right) as a single fraction.

$$\sqrt{16-\frac{4\left(-25\right)}{9}}$$

Multiply 4 and -25 to get -100.

$$\sqrt{16-\frac{-100}{9}}$$

Fraction \frac{-100}{9} can be rewritten as -\frac{100}{9} by extracting the negative sign.

$$\sqrt{16-\left(-\frac{100}{9}\right)}$$

The opposite of -\frac{100}{9} is \frac{100}{9}.

$$\sqrt{16+\frac{100}{9}}$$

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

$$\sqrt{\frac{144}{9}+\frac{100}{9}}$$

Since \frac{144}{9} and \frac{100}{9} have the same denominator, add them by adding their numerators.

$$\sqrt{\frac{144+100}{9}}$$

Add 144 and 100 to get 244.

$$\sqrt{\frac{244}{9}}$$

Rewrite the square root of the division \sqrt{\frac{244}{9}} as the division of square roots \frac{\sqrt{244}}{\sqrt{9}}.

$$\frac{\sqrt{244}}{\sqrt{9}}$$

Factor 244=2^{2}\times 61. Rewrite the square root of the product \sqrt{2^{2}\times 61} as the product of square roots \sqrt{2^{2}}\sqrt{61}. Take the square root of 2^{2}.

$$\frac{2\sqrt{61}}{\sqrt{9}}$$

Calculate the square root of 9 and get 3.

$$\frac{2\sqrt{61}}{3}$$