Solve 4*6.63*10^-34/sqrt{2*9.110^-317.06}

$$\frac{ 4 \cdot 6.63 \times { 10 }^{ -34 } }{ \sqrt{ 2 \cdot 9.1 { 10 }^{ -31 } 7.06 } }$$

Evaluate

$$\frac{51\sqrt{32123}}{12355000000000000000000}\approx 7.398360259 \cdot 10^{-19}$$

Solution Steps

Multiply 4 and 6.63 to get 26.52.

$$\frac{26.52\times 10^{-34}}{\sqrt{2\times 9.1\times 10^{-31}\times 7.06}}$$

Calculate 10 to the power of -34 and get \frac{1}{10000000000000000000000000000000000}.

$$\frac{26.52\times \frac{1}{10000000000000000000000000000000000}}{\sqrt{2\times 9.1\times 10^{-31}\times 7.06}}$$

Multiply 26.52 and \frac{1}{10000000000000000000000000000000000} to get \frac{663}{250000000000000000000000000000000000}.

$$\frac{\frac{663}{250000000000000000000000000000000000}}{\sqrt{2\times 9.1\times 10^{-31}\times 7.06}}$$

Multiply 2 and 9.1 to get 18.2.

$$\frac{\frac{663}{250000000000000000000000000000000000}}{\sqrt{18.2\times 10^{-31}\times 7.06}}$$

Calculate 10 to the power of -31 and get \frac{1}{10000000000000000000000000000000}.

$$\frac{\frac{663}{250000000000000000000000000000000000}}{\sqrt{18.2\times \frac{1}{10000000000000000000000000000000}\times 7.06}}$$

Multiply 18.2 and \frac{1}{10000000000000000000000000000000} to get \frac{91}{50000000000000000000000000000000}.

$$\frac{\frac{663}{250000000000000000000000000000000000}}{\sqrt{\frac{91}{50000000000000000000000000000000}\times 7.06}}$$

Multiply \frac{91}{50000000000000000000000000000000} and 7.06 to get \frac{32123}{2500000000000000000000000000000000}.

$$\frac{\frac{663}{250000000000000000000000000000000000}}{\sqrt{\frac{32123}{2500000000000000000000000000000000}}}$$

Rewrite the square root of the division \sqrt{\frac{32123}{2500000000000000000000000000000000}} as the division of square roots \frac{\sqrt{32123}}{\sqrt{2500000000000000000000000000000000}}.

$$\frac{\frac{663}{250000000000000000000000000000000000}}{\frac{\sqrt{32123}}{\sqrt{2500000000000000000000000000000000}}}$$

Calculate the square root of 2500000000000000000000000000000000 and get 50000000000000000.

$$\frac{\frac{663}{250000000000000000000000000000000000}}{\frac{\sqrt{32123}}{50000000000000000}}$$

Divide \frac{663}{250000000000000000000000000000000000} by \frac{\sqrt{32123}}{50000000000000000} by multiplying \frac{663}{250000000000000000000000000000000000} by the reciprocal of \frac{\sqrt{32123}}{50000000000000000}.

$$\frac{663\times 50000000000000000}{250000000000000000000000000000000000\sqrt{32123}}$$

Cancel out 50000000000000000 in both numerator and denominator.

$$\frac{663}{5000000000000000000\sqrt{32123}}$$

Rationalize the denominator of \frac{663}{5000000000000000000\sqrt{32123}} by multiplying numerator and denominator by \sqrt{32123}.

$$\frac{663\sqrt{32123}}{5000000000000000000\left(\sqrt{32123}\right)^{2}}$$

The square of \sqrt{32123} is 32123.

$$\frac{663\sqrt{32123}}{5000000000000000000\times 32123}$$

Cancel out 13 in both numerator and denominator.

$$\frac{51\sqrt{32123}}{2471\times 5000000000000000000}$$

Multiply 2471 and 5000000000000000000 to get 12355000000000000000000.

$$\frac{51\sqrt{32123}}{12355000000000000000000}$$