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Question
\left(2\sqrt{\frac{11}{3}}\right)-\left(5\sqrt{\frac{3}{11}}\right)
Calculate the value
\frac{7\sqrt{33}}{33}
Alternative Form
\approx 1.218544
Evaluate
\left(2\sqrt{\frac{11}{3}}\right)-\left(5\sqrt{\frac{3}{11}}\right)
Simplify the root
More Steps
Evaluate
\sqrt{\frac{11}{3}}
To take a root of a fraction,take the root of the numerator and denominator separately
\frac{\sqrt{11}}{\sqrt{3}}
Multiply by the Conjugate
\frac{\sqrt{11}\times \sqrt{3}}{\sqrt{3}\times \sqrt{3}}
Multiply the numbers
More Steps
Evaluate
\sqrt{11}\times \sqrt{3}
The product of roots with the same index is equal to the root of the product
\sqrt{11\times 3}
Calculate the product
\sqrt{33}
\frac{\sqrt{33}}{\sqrt{3}\times \sqrt{3}}
When a square root of an expression is multiplied by itself,the result is that expression
\frac{\sqrt{33}}{3}
\left(2\times \frac{\sqrt{33}}{3}\right)-\left(5\sqrt{\frac{3}{11}}\right)
Multiply the numbers
\frac{2\sqrt{33}}{3}-\left(5\sqrt{\frac{3}{11}}\right)
Simplify the root
More Steps
Evaluate
\sqrt{\frac{3}{11}}
To take a root of a fraction,take the root of the numerator and denominator separately
\frac{\sqrt{3}}{\sqrt{11}}
Multiply by the Conjugate
\frac{\sqrt{3}\times \sqrt{11}}{\sqrt{11}\times \sqrt{11}}
Multiply the numbers
More Steps
Evaluate
\sqrt{3}\times \sqrt{11}
The product of roots with the same index is equal to the root of the product
\sqrt{3\times 11}
Calculate the product
\sqrt{33}
\frac{\sqrt{33}}{\sqrt{11}\times \sqrt{11}}
When a square root of an expression is multiplied by itself,the result is that expression
\frac{\sqrt{33}}{11}
\frac{2\sqrt{33}}{3}-\left(5\times \frac{\sqrt{33}}{11}\right)
Multiply the numbers
\frac{2\sqrt{33}}{3}-\frac{5\sqrt{33}}{11}
Reduce fractions to a common denominator
\frac{2\sqrt{33}\times 11}{3\times 11}-\frac{5\sqrt{33}\times 3}{11\times 3}
Multiply the numbers
\frac{2\sqrt{33}\times 11}{33}-\frac{5\sqrt{33}\times 3}{11\times 3}
Multiply the numbers
\frac{2\sqrt{33}\times 11}{33}-\frac{5\sqrt{33}\times 3}{33}
Write all numerators above the common denominator
\frac{2\sqrt{33}\times 11-5\sqrt{33}\times 3}{33}
Multiply the terms
\frac{22\sqrt{33}-5\sqrt{33}\times 3}{33}
Multiply the terms
\frac{22\sqrt{33}-15\sqrt{33}}{33}
Solution
More Steps
Evaluate
22\sqrt{33}-15\sqrt{33}
Collect like terms by calculating the sum or difference of their coefficients
\left(22-15\right)\sqrt{33}
Subtract the numbers
7\sqrt{33}
\frac{7\sqrt{33}}{33}
Alternative Form
\approx 1.218544
Show Solutions
