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Answer :
To determine if 164 is a perfect square, we need to understand what a perfect square is. A perfect square is a number that can be expressed as the square of an integer. In simpler terms, you should be able to find a whole number that, when multiplied by itself, equals 164.
1. Understanding the Concept: For example, 4 is a perfect square because [tex]\(2 \times 2 = 4\)[/tex], and 9 is a perfect square because [tex]\(3 \times 3 = 9\)[/tex]. We need to find out if there is a whole number [tex]\(n\)[/tex] such that [tex]\(n \times n = 164\)[/tex].
2. Finding the Square Root: The way to check this is by calculating the square root of 164 and seeing if it results in a whole number. In our case, the square root of 164 is approximately 12.8062.
3. Checking Wholeness: Since 12.8062 is not a whole number (it has decimal places), there is no integer [tex]\(n\)[/tex] that satisfies [tex]\(n \times n = 164\)[/tex]. Therefore, 164 cannot be expressed as the square of a whole number.
Based on this explanation, we conclude that 164 is not a perfect square. There is no whole number that, when multiplied by itself, gives 164.
1. Understanding the Concept: For example, 4 is a perfect square because [tex]\(2 \times 2 = 4\)[/tex], and 9 is a perfect square because [tex]\(3 \times 3 = 9\)[/tex]. We need to find out if there is a whole number [tex]\(n\)[/tex] such that [tex]\(n \times n = 164\)[/tex].
2. Finding the Square Root: The way to check this is by calculating the square root of 164 and seeing if it results in a whole number. In our case, the square root of 164 is approximately 12.8062.
3. Checking Wholeness: Since 12.8062 is not a whole number (it has decimal places), there is no integer [tex]\(n\)[/tex] that satisfies [tex]\(n \times n = 164\)[/tex]. Therefore, 164 cannot be expressed as the square of a whole number.
Based on this explanation, we conclude that 164 is not a perfect square. There is no whole number that, when multiplied by itself, gives 164.
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