Is 5-3√5-√5 an irrational or rational number?
Understanding the components of the expression is crucial in determining whether the resulting number is rational or irrational.
- Breaking down the expression:
- The expression 5-3√5-√5 can be broken down into three parts: 5, 3√5, and √5.
- 5 is a rational number since it can be expressed as 5/1.
- √5 is an irrational number since it cannot be expressed as a simple fraction.
- 3√5 is also irrational since it involves the square root of an irrational number (5) being multiplied by a rational number (3).
- Combining rational and irrational numbers:
- When we subtract irrational numbers from rational numbers, the result can be either rational or irrational.
- In this case, when we subtract irrational numbers (√5 and 3√5) from a rational number (5), the result is irrational.
- Conclusion:
- The expression 5-3√5-√5 results in an irrational number.
- Therefore, 5-3√5-√5 is an irrational number due to the presence of irrational components in the expression.
In summary, the combination of rational and irrational numbers in the expression leads to the resulting number being irrational. Understanding the nature of each component and how they interact is essential in determining the rationality or irrationality of the final number.