Solve sqrt{3^2+8^2*5^2/5+5}

$$\sqrt{ { 3 }^{ 2 } + { 8 }^{ 2 } \times \frac{ { 5 }^{ 2 } }{ 5+5 } }$$

Evaluate

$$13$$

Solution Steps

Calculate 3 to the power of 2 and get 9.

$$\sqrt{9+8^{2}\times \frac{5^{2}}{5+5}}$$

Calculate 8 to the power of 2 and get 64.

$$\sqrt{9+64\times \frac{5^{2}}{5+5}}$$

Calculate 5 to the power of 2 and get 25.

$$\sqrt{9+64\times \frac{25}{5+5}}$$

Add 5 and 5 to get 10.

$$\sqrt{9+64\times \frac{25}{10}}$$

Reduce the fraction \frac{25}{10} to lowest terms by extracting and canceling out 5.

$$\sqrt{9+64\times \frac{5}{2}}$$

Express 64\times \frac{5}{2} as a single fraction.

$$\sqrt{9+\frac{64\times 5}{2}}$$

Multiply 64 and 5 to get 320.

$$\sqrt{9+\frac{320}{2}}$$

Divide 320 by 2 to get 160.

$$\sqrt{9+160}$$

Add 9 and 160 to get 169.

$$\sqrt{169}$$

Calculate the square root of 169 and get 13.

$$13$$

Factor

$$13$$