Solve =sqrt{8.99*10^9(48*10^-6)/2.7*10^-2}

$$= \sqrt { \frac { 8.99 \times 10 ^ { 9 } ( 48 \times 10 ^ { - 6 } ) } { 2.7 \times 10 ^ { - 2 } } }$$

Evaluate

$$\frac{400\sqrt{899}}{3}\approx 3997.777160151$$

Solution Steps

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

$$\sqrt{\frac{8.99\times 10^{3}\times 48}{2.7\times 10^{-2}}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.

$$\sqrt{\frac{8.99\times 48\times 10^{5}}{2.7}}$$

Multiply 8.99 and 48 to get 431.52.

$$\sqrt{\frac{431.52\times 10^{5}}{2.7}}$$

Calculate 10 to the power of 5 and get 100000.

$$\sqrt{\frac{431.52\times 100000}{2.7}}$$

Multiply 431.52 and 100000 to get 43152000.

$$\sqrt{\frac{43152000}{2.7}}$$

Expand \frac{43152000}{2.7} by multiplying both numerator and the denominator by 10.

$$\sqrt{\frac{431520000}{27}}$$

Reduce the fraction \frac{431520000}{27} to lowest terms by extracting and canceling out 3.

$$\sqrt{\frac{143840000}{9}}$$

Rewrite the square root of the division \sqrt{\frac{143840000}{9}} as the division of square roots \frac{\sqrt{143840000}}{\sqrt{9}}.

$$\frac{\sqrt{143840000}}{\sqrt{9}}$$

Factor 143840000=400^{2}\times 899. Rewrite the square root of the product \sqrt{400^{2}\times 899} as the product of square roots \sqrt{400^{2}}\sqrt{899}. Take the square root of 400^{2}.

$$\frac{400\sqrt{899}}{\sqrt{9}}$$

Calculate the square root of 9 and get 3.

$$\frac{400\sqrt{899}}{3}$$