Read the following statements.
Statement 1: Square root of an irrational numbr is rational.
Statement 2: All those real numbers which are not rational are irrational.

Options

A. Both Statement 1 and Statement 2 are true .
B. Statement 1 is true and Statement 2 is false.
C. Statement 1 is false and Statement 2 is true .
D. Both Statement 1 and Statement 2 are false.

Answer

To solve the problem, we need to analyze the two statements provided and determine their validity.

**Step 1: Analyze Statement 1**
- Statement 1 claims that "the square root of an irrational number is rational."
- Let's consider an example of an irrational number, such as √2.
- If we take the square root of √2, we get (√2)^(1/2) = 2^(1/4), which is still an irrational number.
- Therefore, the square root of an irrational number can also be irrational.

**Conclusion for Statement 1:** This statement is **false**.

**Step 2: Analyze Statement 2**
- Statement 2 claims that "all those real numbers which are not rational are irrational."
- By definition, rational numbers are numbers that can be expressed as a fraction p/q, where p and q are integers and q ≠ 0.
- If a real number is not rational, it must fall into the category of irrational numbers (which cannot be expressed as a fraction).
- Hence, all real numbers that are not rational are indeed irrational.

**Conclusion for Statement 2:** This statement is **true**.

**Final Conclusion:**
- Statement 1 is false, and Statement 2 is true.
- Therefore, the correct answer is that Statement 1 is false and Statement 2 is true.

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