Which among the following numbers is the greates ? `0.07+ sqrt(0.16), sqrt(1.44), 1.02`

Answer

To determine which among the numbers \(0.07 + \sqrt{0.16}\), \(\sqrt{1.44}\), and \(1.02\) is the greatest, we will evaluate each expression step by step.

### Step 1: Calculate \( \sqrt{0.16} \)

To find \( \sqrt{0.16} \):
- We can express \(0.16\) as \(\frac{16}{100}\).
- Therefore, \( \sqrt{0.16} = \sqrt{\frac{16}{100}} = \frac{\sqrt{16}}{\sqrt{100}} = \frac{4}{10} = 0.4\).

**Hint:** Remember that the square root of a fraction can be calculated by taking the square root of the numerator and the denominator separately.

### Step 2: Calculate \( 0.07 + \sqrt{0.16} \)

Now, we can add \(0.07\) and \(0.4\):
- \(0.07 + 0.4 = 0.07 + 0.40 = 0.47\).

**Hint:** When adding decimals, align them by the decimal point to ensure accurate addition.

### Step 3: Calculate \( \sqrt{1.44} \)

Next, we calculate \( \sqrt{1.44} \):
- We can express \(1.44\) as \(\frac{144}{100}\).
- Therefore, \( \sqrt{1.44} = \sqrt{\frac{144}{100}} = \frac{\sqrt{144}}{\sqrt{100}} = \frac{12}{10} = 1.2\).

**Hint:** Similar to the previous step, express the decimal as a fraction to simplify the square root calculation.

### Step 4: Compare the values

Now we have:
- \(0.07 + \sqrt{0.16} = 0.47\)
- \(\sqrt{1.44} = 1.2\)
- \(1.02\)

We need to compare these three values:
- \(0.47\)
- \(1.2\)
- \(1.02\)

Clearly, \(1.2\) is greater than both \(0.47\) and \(1.02\).

### Conclusion

Thus, the greatest number among \(0.07 + \sqrt{0.16}\), \(\sqrt{1.44}\), and \(1.02\) is \(\sqrt{1.44} = 1.2\).

**Final Answer:** The greatest number is \(1.2\).

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