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Compare [tex]\sqrt{140}[/tex] and 103 using <, >, or =.

A. [tex]\sqrt{140} > 103[/tex]

B. [tex]\sqrt{140} = 103[/tex]

C. [tex]\sqrt{140} < 103[/tex]

Answer :

Final answer:

When comparing √140 to 10³ (1000), we conclude that √140, which is less than 12, is much smaller than 1000. Therefore, the correct inequality is √140 < 10³.

Explanation:

The question requires comparing the square root of 140 with 10³. To make the comparison clearer, we can first estimate √140. Since √100 = 10 and √144 = 12 (144 being the nearest perfect square to 140), √140 must be between 10 and 12. In fact, it's closer to 12 because 140 is near 144. So we can say with certainty that √140 < 12. Now comparing √140 to 10³, which is 1000, it's clear that √140 is much smaller. Therefore, √140 < 10³.

Comparing numbers of different forms, like a square root and an exponent, sometimes requires estimation or conversion to similar forms. In this case, since both numbers are positive, comparing their sizes is straightforward once we've estimated the square root. Remember that when using approximations like √140 ≈ 12, we're using the 'approximately equal' sign (≈), not to be confused with the 'equal' sign (=), as minor differences may exist that do not impact the inequality.

In conclusion, based on the given estimated comparison, the correct answer would be:

  • √140 < 103

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