Question : Out of the numbers 0.3, 0.03, 0.9, and 0.09, the number that is nearest to the value of $\sqrt{0.9}$ is:
Option 1: 0.3
Option 2: 0.03
Option 3: 0.9
Option 4: 0.09
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Correct Answer: 0.9
Solution :
The value of $\sqrt{0.9}= \sqrt{\frac{9}{10}}$
= ${\frac{3}{\sqrt{10}}}$
= ${\frac{3\sqrt{10}}{10}}$
$\sqrt{10}$ is greater than 3 but less than 4.
So, 9 < 3$\sqrt{10}$ < 10
⇒ 0.9 < ${\frac{3\sqrt{10}}{10}}$ < 1
⇒ 0.9 < $\sqrt{0.9}$ < 1
Hence, the correct answer is 0.9.
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