Solve (2 sqrt(3 / 11)) - (5 sqrt(11 / 3))

Question

Calculate the value

- \frac{49 33}{33}

Alternative Form

\approx - 8.529805

Evaluate

(2 \frac{3}{11}) - (5 \frac{11}{3})

Simplify the root

More Steps

Evaluate

\frac{3}{11}

To take a root of a fraction,take the root of the numerator and denominator separately

\frac{3}{11}

Multiply by the Conjugate

\frac{3 \times 11}{11 \times 11}

Multiply the numbers

More Steps

Evaluate

3 \times 11

The product of roots with the same index is equal to the root of the product

3 \times 11

Calculate the product

33

\frac{33}{11 \times 11}

When a square root of an expression is multiplied by itself,the result is that expression

\frac{33}{11}

(2 \times \frac{33}{11}) - (5 \frac{11}{3})

Multiply the numbers

\frac{2 33}{11} - (5 \frac{11}{3})

Simplify the root

More Steps

Evaluate

\frac{11}{3}

To take a root of a fraction,take the root of the numerator and denominator separately

\frac{11}{3}

Multiply by the Conjugate

\frac{11 \times 3}{3 \times 3}

Multiply the numbers

More Steps

Evaluate

11 \times 3

The product of roots with the same index is equal to the root of the product

11 \times 3

Calculate the product

33

\frac{33}{3 \times 3}

When a square root of an expression is multiplied by itself,the result is that expression

\frac{33}{3}

\frac{2 33}{11} - (5 \times \frac{33}{3})

Multiply the numbers

\frac{2 33}{11} - \frac{5 33}{3}

Reduce fractions to a common denominator

\frac{2 33 \times 3}{11 \times 3} - \frac{5 33 \times 11}{3 \times 11}

Multiply the numbers

\frac{2 33 \times 3}{33} - \frac{5 33 \times 11}{3 \times 11}

Multiply the numbers

\frac{2 33 \times 3}{33} - \frac{5 33 \times 11}{33}

Write all numerators above the common denominator

\frac{2 33 \times 3 - 5 33 \times 11}{33}

Multiply the terms

\frac{6 33 - 5 33 \times 11}{33}

Multiply the terms

\frac{6 33 - 55 33}{33}

Subtract the numbers

More Steps

Evaluate

633 - 5533

Collect like terms by calculating the sum or difference of their coefficients

(6 - 55) 33

Subtract the numbers

- 4933

\frac{- 49 33}{33}

Solution

- \frac{49 33}{33}

Alternative Form

\approx - 8.529805

Show Solution