√(7/9 - 1 1/2) ifadəsini hesablayın.

Steps to Solve

1. Convert Mixed Number to Improper Fraction

   First, convert the mixed number $1 \frac{1}{2}$ to an improper fraction.

   $$ 1 \frac{1}{2} = \frac{3}{2} $$

2. Substitute and Simplify Inside the Radical

   Substitute $\frac{3}{2}$ back into the expression. Now, simplify the expression inside the square root:

   $$ \frac{7}{9} - \frac{3}{2} $$

   To perform this subtraction, find a common denominator. The least common multiple of 9 and 2 is 18.

   Converting each fraction:

   $$ \frac{7}{9} = \frac{14}{18} $$ \ $$ \frac{3}{2} = \frac{27}{18} $$

   Now, perform the subtraction:

   $$ \frac{14}{18} - \frac{27}{18} = \frac{14 - 27}{18} = \frac{-13}{18} $$

3. Take the Square Root

   Now, we take the square root of the result:

   $$ \sqrt{\frac{-13}{18}} $$

   Since the number under the square root is negative, we can express it as:

   $$ \sqrt{-1} \cdot \sqrt{\frac{13}{18}} = i \sqrt{\frac{13}{18}} $$

4. Simplify the Square Root Further

   Here, we can simplify the square root:

   $$ \sqrt{\frac{13}{18}} = \frac{\sqrt{13}}{\sqrt{18}} = \frac{\sqrt{13}}{3\sqrt{2}} $$

   Thus, the final result is:

   $$ i \frac{\sqrt{13}}{3\sqrt{2}} $$