Solve sqrt{7.2^2*left(10^-3right)^2+54^2+{left({10}^-3right)}^2}

$$\sqrt{ { 7.2 }^{ 2 } \times { \left( { 10 }^{ -3 } \right) }^{ 2 } + { 54 }^{ 2 } + { \left( { 10 }^{ -3 } \right) }^{ 2 } }$$

Evaluate

$$\frac{7\sqrt{1487755129}}{5000}\approx 54.000000489$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply -3 and 2 to get -6.

$$\sqrt{7.2^{2}\times 10^{-6}+54^{2}+\left(10^{-3}\right)^{2}}$$

To raise a power to another power, multiply the exponents. Multiply -3 and 2 to get -6.

$$\sqrt{7.2^{2}\times 10^{-6}+54^{2}+10^{-6}}$$

Calculate 7.2 to the power of 2 and get 51.84.

$$\sqrt{51.84\times 10^{-6}+54^{2}+10^{-6}}$$

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

$$\sqrt{51.84\times \frac{1}{1000000}+54^{2}+10^{-6}}$$

Multiply 51.84 and \frac{1}{1000000} to get \frac{81}{1562500}.

$$\sqrt{\frac{81}{1562500}+54^{2}+10^{-6}}$$

Calculate 54 to the power of 2 and get 2916.

$$\sqrt{\frac{81}{1562500}+2916+10^{-6}}$$

Add \frac{81}{1562500} and 2916 to get \frac{4556250081}{1562500}.

$$\sqrt{\frac{4556250081}{1562500}+10^{-6}}$$

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

$$\sqrt{\frac{4556250081}{1562500}+\frac{1}{1000000}}$$

Add \frac{4556250081}{1562500} and \frac{1}{1000000} to get \frac{72900001321}{25000000}.

$$\sqrt{\frac{72900001321}{25000000}}$$

Rewrite the square root of the division \sqrt{\frac{72900001321}{25000000}} as the division of square roots \frac{\sqrt{72900001321}}{\sqrt{25000000}}.

$$\frac{\sqrt{72900001321}}{\sqrt{25000000}}$$

Factor 72900001321=7^{2}\times 1487755129. Rewrite the square root of the product \sqrt{7^{2}\times 1487755129} as the product of square roots \sqrt{7^{2}}\sqrt{1487755129}. Take the square root of 7^{2}.

$$\frac{7\sqrt{1487755129}}{\sqrt{25000000}}$$

Calculate the square root of 25000000 and get 5000.

$$\frac{7\sqrt{1487755129}}{5000}$$