1. \( \sqrt{\frac{7}{9}} - \frac{1}{2} \) ifadəsini hesablayın.
Understand the Problem
Sual,
aşağıdakı ifadəni hesablamağımızı tələb edir: ( \sqrt{\frac{7}{9}} - \frac{1}{2} ). Bu ifadəni hesablamaq üçün ilk növbədə kök içərisindəki ifadəni simplifikasiya edəcəyik.
Answer
The expression evaluates to $$ \frac{2\sqrt{7} - 3}{6}. $$
Answer for screen readers
The final answer is $$ \frac{2\sqrt{7} - 3}{6}. $$
Steps to Solve
- Simplification of the square root
We start by simplifying the term inside the square root: $$ \sqrt{\frac{7}{9}} = \frac{\sqrt{7}}{\sqrt{9}} = \frac{\sqrt{7}}{3}. $$
- Rewrite the expression
Now we rewrite the expression: $$ \frac{\sqrt{7}}{3} - \frac{1}{2}. $$
- Finding a common denominator
To subtract the fractions, we need a common denominator, which is 6: $$ \frac{\sqrt{7}}{3} = \frac{2\sqrt{7}}{6}, $$ and $$ \frac{1}{2} = \frac{3}{6}. $$
- Perform the subtraction
Now we can perform the subtraction: $$ \frac{2\sqrt{7}}{6} - \frac{3}{6} = \frac{2\sqrt{7} - 3}{6}. $$
- Final expression
Thus, the final answer is given by: $$ \frac{2\sqrt{7} - 3}{6}. $$
The final answer is $$ \frac{2\sqrt{7} - 3}{6}. $$
More Information
The expression represents a mathematical operation involving square roots and fractions. The answer shows how to manage subtraction of fractions with different denominators.
Tips
- Forgetting to simplify the square root before combining terms.
- Not finding a common denominator correctly.
- Miscalculating during the subtraction process.
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