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Question
2\sqrt{\frac{300}{\pi }}
Calculate the value
\frac{20\sqrt{3\pi }}{\pi }
Alternative Form
\approx 19.5441
Evaluate
2\sqrt{\frac{300}{\pi }}
Simplify the root
More Steps
Evaluate
\sqrt{\frac{300}{\pi }}
To take a root of a fraction,take the root of the numerator and denominator separately
\frac{\sqrt{300}}{\sqrt{\pi }}
Simplify the radical expression
More Steps
Evaluate
\sqrt{300}
Write the expression as a product where the root of one of the factors can be evaluated
\sqrt{100\times 3}
\text{Write the number in exponential form with the base of }10
\sqrt{10^{2}\times 3}
The root of a product is equal to the product of the roots of each factor
\sqrt{10^{2}}\times \sqrt{3}
\text{Reduce the index of the radical and exponent with }2
10\sqrt{3}
\frac{10\sqrt{3}}{\sqrt{\pi }}
Multiply by the Conjugate
\frac{10\sqrt{3}\times \sqrt{\pi }}{\sqrt{\pi }\times \sqrt{\pi }}
The product of roots with the same index is equal to the root of the product
\frac{10\sqrt{3\pi }}{\sqrt{\pi }\times \sqrt{\pi }}
When a square root of an expression is multiplied by itself,the result is that expression
\frac{10\sqrt{3\pi }}{\pi }
2\times \frac{10\sqrt{3\pi }}{\pi }
Multiply the numbers
\frac{2\times 10\sqrt{3\pi }}{\pi }
Solution
\frac{20\sqrt{3\pi }}{\pi }
Alternative Form
\approx 19.5441
Show Solutions
