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

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

Evaluate

$$15\sqrt{1003}\approx 475.052628663$$

Solution Steps

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

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

Calculate 135 to the power of 2 and get 18225.

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

The square of \sqrt{2} is 2.

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

Multiply 18225 and 2 to get 36450.

$$\sqrt{36450+435^{2}}$$

Calculate 435 to the power of 2 and get 189225.

$$\sqrt{36450+189225}$$

Add 36450 and 189225 to get 225675.

$$\sqrt{225675}$$

Factor 225675=15^{2}\times 1003. Rewrite the square root of the product \sqrt{15^{2}\times 1003} as the product of square roots \sqrt{15^{2}}\sqrt{1003}. Take the square root of 15^{2}.

$$15\sqrt{1003}$$