Question

which statements are true? select the five correct answers.

\\(\sqrt{1.8} < 1.8\\)

\\(\sqrt{1.8} > 1\\)

\\(\sqrt{1.8} < \sqrt{1.9}\\)

\\(1.3 < \sqrt{1.8} < 1.4\\)

\\(\sqrt{1.9} + \sqrt{1.8} > 2\\)

\\(\sqrt{1.9} - \sqrt{1.8} > 0.1\\)

Explanation:

Evaluate the first three statements

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Evaluate the fourth and fifth statements

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Evaluate the sixth statement

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Since we need five correct answers, let's re-evaluate Statement 6 or check if there is a typo in the question's options. Let's calculate the values directly:

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Wait, let's look closely at the image.
The fourth statement is \(13 < \sqrt{18} < 14\)? No, it might be \(1.3 < \sqrt{1.8} < 1.4\).
If it is \(1.3 < \sqrt{1.8} < 1.4\):

$$ 1.3^2 = 1.69, \quad 1.4^2 = 1.96 $$

Since \(1.69 < 1.8 < 1.96\), this statement \(1.3 < \sqrt{1.8} < 1.4\) is indeed True.
This gives exactly five true statements: 1, 2, 3, 4 (read as \(1.3 < \sqrt{1.8} < 1.4\)), and 5.

Answer:

• (A) \(\sqrt{1.8} < 1.8\) (Correct answer)
• (B) \(\sqrt{18} > 1\) (Correct answer)
• (C) \(\sqrt{1.8} < \sqrt{1.9}\) (Correct answer)
• (D) \(1.3 < \sqrt{1.8} < 1.4\) (Correct answer)
• (E) \(\sqrt{1.9} + \sqrt{1.8} > 2\) (Correct answer)
• (F) \(\sqrt{1.9} - \sqrt{1.8} > 0.1\)