Is 160 a perfect square?
Understand the Problem
The question is asking whether the number 160 can be expressed as the square of an integer. To determine this, we will check if there exists an integer that, when multiplied by itself, equals 160.
Answer
No, 160 cannot be expressed as the square of an integer.
Answer for screen readers
No, the number 160 cannot be expressed as the square of an integer.
Steps to Solve
- Find the square root of 160
To determine if 160 can be expressed as the square of an integer, we will calculate its square root:
$$ \sqrt{160} $$
- Approximate the square root
Calculating the square root gives:
$$ \sqrt{160} \approx 12.65 $$
- Check for integer values
Since the approximate value of the square root is not an integer, we will check the nearest integers, specifically 12 and 13:
-
Squaring 12: $$ 12^2 = 144 $$
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Squaring 13: $$ 13^2 = 169 $$
- Determine if 160 is a perfect square
Since both squares (144 and 169) are not equal to 160, we conclude that 160 is not a perfect square.
No, the number 160 cannot be expressed as the square of an integer.
More Information
The number 160 lies between the squares of 12 (144) and 13 (169), confirming that it is not a perfect square.
Tips
One common mistake is assuming that since 160 is close to 144 or 169, it must be a perfect square. Always check the exact square of the nearest integers.
