Solve sqrt{{left(-60sqrt{3+1}right)}^2+60^2}

$$\sqrt{ { \left(-60 \sqrt{ 3+1 } \right) }^{ 2 } + { 60 }^{ 2 } }$$

Evaluate

$$60\sqrt{5}\approx 134.16407865$$

Solution Steps

Add 3 and 1 to get 4.

$$\sqrt{\left(-60\sqrt{4}\right)^{2}+60^{2}}$$

Calculate the square root of 4 and get 2.

$$\sqrt{\left(-60\times 2\right)^{2}+60^{2}}$$

Multiply -60 and 2 to get -120.

$$\sqrt{\left(-120\right)^{2}+60^{2}}$$

Calculate -120 to the power of 2 and get 14400.

$$\sqrt{14400+60^{2}}$$

Calculate 60 to the power of 2 and get 3600.

$$\sqrt{14400+3600}$$

Add 14400 and 3600 to get 18000.

$$\sqrt{18000}$$

Factor 18000=60^{2}\times 5. Rewrite the square root of the product \sqrt{60^{2}\times 5} as the product of square roots \sqrt{60^{2}}\sqrt{5}. Take the square root of 60^{2}.

$$60\sqrt{5}$$