Solve sqrt{72^2+54^210^-6}

$$\sqrt{ { 72 }^{ 2 } + { 54 }^{ 2 } { 10 }^{ -6 } }$$

Evaluate

$$\frac{9\sqrt{16000009}}{500}\approx 72.00002025$$

Solution Steps

Calculate 72 to the power of 2 and get 5184.

$$\sqrt{5184+54^{2}\times 10^{-6}}$$

Calculate 54 to the power of 2 and get 2916.

$$\sqrt{5184+2916\times 10^{-6}}$$

Calculate 10 to the power of -6 and get \frac{1}{1000000}.

$$\sqrt{5184+2916\times \frac{1}{1000000}}$$

Multiply 2916 and \frac{1}{1000000} to get \frac{729}{250000}.

$$\sqrt{5184+\frac{729}{250000}}$$

Add 5184 and \frac{729}{250000} to get \frac{1296000729}{250000}.

$$\sqrt{\frac{1296000729}{250000}}$$

Rewrite the square root of the division \sqrt{\frac{1296000729}{250000}} as the division of square roots \frac{\sqrt{1296000729}}{\sqrt{250000}}.

$$\frac{\sqrt{1296000729}}{\sqrt{250000}}$$

Factor 1296000729=9^{2}\times 16000009. Rewrite the square root of the product \sqrt{9^{2}\times 16000009} as the product of square roots \sqrt{9^{2}}\sqrt{16000009}. Take the square root of 9^{2}.

$$\frac{9\sqrt{16000009}}{\sqrt{250000}}$$

Calculate the square root of 250000 and get 500.

$$\frac{9\sqrt{16000009}}{500}$$