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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