Solve sqrt{576-2*24*15+225}+sqrt{2,5^2-2,4^2}

$$\sqrt { 576 - 2 \cdot 24 \cdot 15 + 225 } + \sqrt { 2,5 ^ { 2 } - 2,4 ^ { 2 } }$$

Evaluate

$$3\left(\sqrt{2}+3\right)\approx 13.242640687$$

Solution Steps

Multiply 2 and 24 to get 48.

$$\sqrt{576-48\times 15+225}+\sqrt{2\times 5^{2}-2\times 4^{2}}$$

Multiply 48 and 15 to get 720.

$$\sqrt{576-720+225}+\sqrt{2\times 5^{2}-2\times 4^{2}}$$

Subtract 720 from 576 to get -144.

$$\sqrt{-144+225}+\sqrt{2\times 5^{2}-2\times 4^{2}}$$

Add -144 and 225 to get 81.

$$\sqrt{81}+\sqrt{2\times 5^{2}-2\times 4^{2}}$$

Calculate the square root of 81 and get 9.

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

Calculate 5 to the power of 2 and get 25.

$$9+\sqrt{2\times 25-2\times 4^{2}}$$

Multiply 2 and 25 to get 50.

$$9+\sqrt{50-2\times 4^{2}}$$

Calculate 4 to the power of 2 and get 16.

$$9+\sqrt{50-2\times 16}$$

Multiply 2 and 16 to get 32.

$$9+\sqrt{50-32}$$

Subtract 32 from 50 to get 18.

$$9+\sqrt{18}$$

Factor 18=3^{2}\times 2. Rewrite the square root of the product \sqrt{3^{2}\times 2} as the product of square roots \sqrt{3^{2}}\sqrt{2}. Take the square root of 3^{2}.

$$9+3\sqrt{2}$$