Solve sqrt{{left(135sqrt{3}right)}^2+435^2}

$$\sqrt{ { \left(135 \sqrt{ 3 } \right) }^{ 2 } + { 435 }^{ 2 } }$$

Evaluate

$$30\sqrt{271}\approx 493.862328995$$

Solution Steps

Expand \left(135\sqrt{3}\right)^{2}.

$$\sqrt{135^{2}\left(\sqrt{3}\right)^{2}+435^{2}}$$

Calculate 135 to the power of 2 and get 18225.

$$\sqrt{18225\left(\sqrt{3}\right)^{2}+435^{2}}$$

The square of \sqrt{3} is 3.

$$\sqrt{18225\times 3+435^{2}}$$

Multiply 18225 and 3 to get 54675.

$$\sqrt{54675+435^{2}}$$

Calculate 435 to the power of 2 and get 189225.

$$\sqrt{54675+189225}$$

Add 54675 and 189225 to get 243900.

$$\sqrt{243900}$$

Factor 243900=30^{2}\times 271. Rewrite the square root of the product \sqrt{30^{2}\times 271} as the product of square roots \sqrt{30^{2}}\sqrt{271}. Take the square root of 30^{2}.

$$30\sqrt{271}$$