Which is greater: √45 or √49 - 1?
√45
To determine which value is greater: \( \sqrt{45} \) or \( \sqrt{49} - 1 \), let's evaluate each expression step-by-step.
Calculate the value of \( \sqrt{45} \):
\( \sqrt{45} = \sqrt{9 \times 5} = \sqrt{9} \times \sqrt{5} = 3 \times \sqrt{5} \)
Approximating \(\sqrt{5} \approx 2.236\), we get:
\( \sqrt{45} \approx 3 \times 2.236 = 6.708 \)
Calculate the value of \( \sqrt{49} - 1 \):
\( \sqrt{49} = 7 \) (since 49 is a perfect square) and thus:
\( \sqrt{49} - 1 = 7 - 1 = 6 \)
Comparison:
\( \sqrt{45} \approx 6.708 \) and \( \sqrt{49} - 1 = 6 \)
Clearly, \( 6.708 > 6 \), which implies \( \sqrt{45} \) is greater than \( \sqrt{49} - 1 \).
Therefore, the correct answer is \( \sqrt{45} \).
This confirms that the choice \(√\)45 is the greater value compared to \(√\)49 - 1.
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