Solve sqrt{8,99*10^9*3*10^-6/4}=

$$\sqrt { \frac { 8,99 \cdot 10 ^ { 9 } \cdot 3 \cdot 10 ^ { - 6 } } { 4 } } =$$

Evaluate

$$\frac{\sqrt{26970}}{2}\approx 82.112727394$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 9 and -6 to get 3.

$$\sqrt{\frac{8,99\times 10^{3}\times 3}{4}}$$

Calculate 10 to the power of 3 and get 1000.

$$\sqrt{\frac{8,99\times 1000\times 3}{4}}$$

Multiply 8,99 and 1000 to get 8990.

$$\sqrt{\frac{8990\times 3}{4}}$$

Multiply 8990 and 3 to get 26970.

$$\sqrt{\frac{26970}{4}}$$

Reduce the fraction \frac{26970}{4} to lowest terms by extracting and canceling out 2.

$$\sqrt{\frac{13485}{2}}$$

Rewrite the square root of the division \sqrt{\frac{13485}{2}} as the division of square roots \frac{\sqrt{13485}}{\sqrt{2}}.

$$\frac{\sqrt{13485}}{\sqrt{2}}$$

Rationalize the denominator of \frac{\sqrt{13485}}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{\sqrt{13485}\sqrt{2}}{\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$\frac{\sqrt{13485}\sqrt{2}}{2}$$

To multiply \sqrt{13485} and \sqrt{2}, multiply the numbers under the square root.

$$\frac{\sqrt{26970}}{2}$$