Solve sqrt{100^2-35^2}*cos30^circ

$$\sqrt { 100 ^ { 2 } - 35 ^ { 2 } } \times \cos 30 ^ { \circ }$$

Evaluate

$$\frac{45\sqrt{13}}{2}\approx 81.124903698$$

Solution Steps

Calculate 100 to the power of 2 and get 10000.

$$\sqrt{10000-35^{2}}\cos(30)$$

Calculate 35 to the power of 2 and get 1225.

$$\sqrt{10000-1225}\cos(30)$$

Subtract 1225 from 10000 to get 8775.

$$\sqrt{8775}\cos(30)$$

Factor 8775=15^{2}\times 39. Rewrite the square root of the product \sqrt{15^{2}\times 39} as the product of square roots \sqrt{15^{2}}\sqrt{39}. Take the square root of 15^{2}.

$$15\sqrt{39}\cos(30)$$

Get the value of \cos(30) from trigonometric values table.

$$15\sqrt{39}\times \frac{\sqrt{3}}{2}$$

Express 15\times \frac{\sqrt{3}}{2} as a single fraction.

$$\frac{15\sqrt{3}}{2}\sqrt{39}$$

Express \frac{15\sqrt{3}}{2}\sqrt{39} as a single fraction.

$$\frac{15\sqrt{3}\sqrt{39}}{2}$$

Factor 39=3\times 13. Rewrite the square root of the product \sqrt{3\times 13} as the product of square roots \sqrt{3}\sqrt{13}.

$$\frac{15\sqrt{3}\sqrt{3}\sqrt{13}}{2}$$

Multiply \sqrt{3} and \sqrt{3} to get 3.

$$\frac{15\times 3\sqrt{13}}{2}$$

Multiply 15 and 3 to get 45.

$$\frac{45\sqrt{13}}{2}$$