Final answer:
To simplify the expression √2/9 - 3√8/9 + √32/9, we can simplify each square root and then combine like terms, resulting in the simplified expression of -√2/9.
Step-by-step explanation:
The question involves simplifying a mathematical expression containing square roots and fractions. To simplify √2/9 - 3√8/9 + √32/9, we need to simplify each square root separately. Recognize that √8 and √32 can be expressed with square root factors that are perfect squares:
- √2/9 remains as is because 2 is a prime number.
- 3√8/9 = 3√(4×2)/9 = 3√4 * √2/9 = 3*2√2/9 = 6√2/9
- √32/9 = √(16×2)/9 = √16 * √2/9 = 4√2/9
Now combine the terms:
√2/9 - 6√2/9 + 4√2/9 = (√2 - 6√2 + 4√2) / 9 = (-√2) / 9
Thus, the simplified expression is -√2/9.