Solve sqrt{25^2-24^2}*sqrt{3^2+4^2}

$$\sqrt { 25 ^ { 2 } - 24 ^ { 2 } } \times \sqrt { 3 ^ { 2 } + 4 ^ { 2 } }$$

Evaluate

$$35$$

Solution Steps

Calculate 25 to the power of 2 and get 625.

$$\sqrt{625-24^{2}}\sqrt{3^{2}+4^{2}}$$

Calculate 24 to the power of 2 and get 576.

$$\sqrt{625-576}\sqrt{3^{2}+4^{2}}$$

Subtract 576 from 625 to get 49.

$$\sqrt{49}\sqrt{3^{2}+4^{2}}$$

Calculate the square root of 49 and get 7.

$$7\sqrt{3^{2}+4^{2}}$$

Calculate 3 to the power of 2 and get 9.

$$7\sqrt{9+4^{2}}$$

Calculate 4 to the power of 2 and get 16.

$$7\sqrt{9+16}$$

Add 9 and 16 to get 25.

$$7\sqrt{25}$$

Calculate the square root of 25 and get 5.

$$7\times 5$$

Multiply 7 and 5 to get 35.

$$35$$

Factor

$$5\times 7$$