Find which of the variables `x, y, z` and `u` represent rational numbers and which irrational numbers:(i) `x^2=5` (ii) `y^2=9`(iii)`z^2=0.04`(iv) `u^2=17/4`

Explanation

To determine which of the variables \(x\), \(y\), \(z\), and \(u\) represent rational numbers and which represent irrational numbers, we will analyze each equation step by step.

### Step 1: Analyze \(x^2 = 5\)

1. To find \(x\), we take the square root of both sides:
\[ x = \pm \sqrt{5} \]
2. The number \(\sqrt{5}\) is an irrational number because it cannot be expressed as a fraction of two integers (it is a non-terminating, non-repeating decimal).

**Conclusion**: \(x\) is an **irrational number**.

### Step 2: Analyze \(y^2 = 9\)

1. To find \(y\), we take the square root of both sides:
\[ y = \pm \sqrt{9} \]
2. Since \(\sqrt{9} = 3\), which can be expressed as \(\frac{3}{1}\), it is a rational number.

**Conclusion**: \(y\) is a **rational number**.

### Step 3: Analyze \(z^2 = 0.04\)

1. To find \(z\), we take the square root of both sides:
\[ z = \pm \sqrt{0.04} \]
2. We can express \(0.04\) as \(\frac{4}{100} = \frac{1}{25}\). Thus,
\[ z = \pm \sqrt{\frac{1}{25}} = \pm \frac{1}{5} \]
3. Since \(\frac{1}{5}\) is a fraction of two integers, it is a rational number.

**Conclusion**: \(z\) is a **rational number**.

### Step 4: Analyze \(u^2 = \frac{17}{4}\)

1. To find \(u\), we take the square root of both sides:
\[ u = \pm \sqrt{\frac{17}{4}} = \pm \frac{\sqrt{17}}{2} \]
2. The number \(\sqrt{17}\) is irrational because it cannot be expressed as a fraction of two integers.

**Conclusion**: \(u\) is an **irrational number**.

### Final Summary:
- \(x\): Irrational
- \(y\): Rational
- \(z\): Rational
- \(u\): Irrational

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