Solve =frac{10^-2*sqrt{3}}{sqrt{27}+sqrt{48}+sqrt{507}}

$$= \frac { 10 ^ { - 2 } \times \sqrt { 3 } } { \sqrt { 27 } + \sqrt { 48 } + \sqrt { 507 } }$$

Evaluate

$$\frac{1}{2000}=0.0005$$

Solution Steps

Calculate 10 to the power of -2 and get \frac{1}{100}.

$$\frac{\frac{1}{100}\sqrt{3}}{\sqrt{27}+\sqrt{48}+\sqrt{507}}$$

Factor 27=3^{2}\times 3. Rewrite the square root of the product \sqrt{3^{2}\times 3} as the product of square roots \sqrt{3^{2}}\sqrt{3}. Take the square root of 3^{2}.

$$\frac{\frac{1}{100}\sqrt{3}}{3\sqrt{3}+\sqrt{48}+\sqrt{507}}$$

Factor 48=4^{2}\times 3. Rewrite the square root of the product \sqrt{4^{2}\times 3} as the product of square roots \sqrt{4^{2}}\sqrt{3}. Take the square root of 4^{2}.

$$\frac{\frac{1}{100}\sqrt{3}}{3\sqrt{3}+4\sqrt{3}+\sqrt{507}}$$

Combine 3\sqrt{3} and 4\sqrt{3} to get 7\sqrt{3}.

$$\frac{\frac{1}{100}\sqrt{3}}{7\sqrt{3}+\sqrt{507}}$$

Factor 507=13^{2}\times 3. Rewrite the square root of the product \sqrt{13^{2}\times 3} as the product of square roots \sqrt{13^{2}}\sqrt{3}. Take the square root of 13^{2}.

$$\frac{\frac{1}{100}\sqrt{3}}{7\sqrt{3}+13\sqrt{3}}$$

Combine 7\sqrt{3} and 13\sqrt{3} to get 20\sqrt{3}.

$$\frac{\frac{1}{100}\sqrt{3}}{20\sqrt{3}}$$

Cancel out \sqrt{3} in both numerator and denominator.

$$\frac{\frac{1}{100}}{20}$$

Express \frac{\frac{1}{100}}{20} as a single fraction.

$$\frac{1}{100\times 20}$$

Multiply 100 and 20 to get 2000.

$$\frac{1}{2000}$$

Factor

$$\frac{1}{2 ^ {4} \cdot 5 ^ {3}} = 0.0005$$