Solve sqrt{9.8*6.38*left(10^2right)^2^2}

$$\sqrt{ 9.8 \times 6.38 \times { \left( { 10 }^{ 2 } \right) }^{ { 2 }^{ 2 } } }$$

Evaluate

$$1400\sqrt{3190}\approx 79072.11898008$$

Solution Steps

Multiply 9.8 and 6.38 to get 62.524.

$$\sqrt{62.524\times \left(10^{2}\right)^{2^{2}}}$$

Calculate 10 to the power of 2 and get 100.

$$\sqrt{62.524\times 100^{2^{2}}}$$

Calculate 2 to the power of 2 and get 4.

$$\sqrt{62.524\times 100^{4}}$$

Calculate 100 to the power of 4 and get 100000000.

$$\sqrt{62.524\times 100000000}$$

Multiply 62.524 and 100000000 to get 6252400000.

$$\sqrt{6252400000}$$

Factor 6252400000=1400^{2}\times 3190. Rewrite the square root of the product \sqrt{1400^{2}\times 3190} as the product of square roots \sqrt{1400^{2}}\sqrt{3190}. Take the square root of 1400^{2}.

$$1400\sqrt{3190}$$