Solve sqrt{7^2*13^2-7^2*5^2}

$$\sqrt{ { 7 }^{ 2 } \times { 13 }^{ 2 } - { 7 }^{ 2 } \times { 5 }^{ 2 } }$$

Evaluate

$$84$$

Solution Steps

Calculate 7 to the power of 2 and get 49.

$$\sqrt{49\times 13^{2}-7^{2}\times 5^{2}}$$

Calculate 13 to the power of 2 and get 169.

$$\sqrt{49\times 169-7^{2}\times 5^{2}}$$

Multiply 49 and 169 to get 8281.

$$\sqrt{8281-7^{2}\times 5^{2}}$$

Calculate 7 to the power of 2 and get 49.

$$\sqrt{8281-49\times 5^{2}}$$

Calculate 5 to the power of 2 and get 25.

$$\sqrt{8281-49\times 25}$$

Multiply 49 and 25 to get 1225.

$$\sqrt{8281-1225}$$

Subtract 1225 from 8281 to get 7056.

$$\sqrt{7056}$$

Calculate the square root of 7056 and get 84.

$$84$$

Factor

$$2^{2}\times 3\times 7$$