Solve sqrt{24^2+16^2+4^2}

$$\sqrt{ { 24 }^{ 2 } + { 16 }^{ 2 } + { 4 }^{ 2 } }$$

Evaluate

$$4\sqrt{53}\approx 29.120439557$$

Solution Steps

Calculate 24 to the power of 2 and get 576.

$$\sqrt{576+16^{2}+4^{2}}$$

Calculate 16 to the power of 2 and get 256.

$$\sqrt{576+256+4^{2}}$$

Add 576 and 256 to get 832.

$$\sqrt{832+4^{2}}$$

Calculate 4 to the power of 2 and get 16.

$$\sqrt{832+16}$$

Add 832 and 16 to get 848.

$$\sqrt{848}$$

Factor 848=4^{2}\times 53. Rewrite the square root of the product \sqrt{4^{2}\times 53} as the product of square roots \sqrt{4^{2}}\sqrt{53}. Take the square root of 4^{2}.

$$4\sqrt{53}$$