Answer :
Let's examine each of the given numbers to determine whether they are perfect squares or not.
### a) 1296
First, we find the square root of 1296. The square root of 1296 is found to be 36. We check if squaring 36 gives us back 1296:
[tex]\[ 36 \times 36 = 1296 \][/tex]
Since 1296 equals the square of 36, it confirms that 1296 is a perfect square.
### b) 1000
Next, let's consider 1000. We estimate the square root of 1000 and find it is approximately 31.62. We then check the integers close to this value, which are 31 and 32, to see if squaring either of them results in 1000:
[tex]\[ 31 \times 31 = 961 \][/tex]
[tex]\[ 32 \times 32 = 1024 \][/tex]
Neither 961 nor 1024 equals 1000. Therefore, 1000 is not a perfect square.
### c) 373758
Now, let's look at 373758. Estimating the square root gives a value around 611.28. We check the integers 611 and 612:
[tex]\[ 611 \times 611 = 373321 \][/tex]
[tex]\[ 612 \times 612 = 374544 \][/tex]
Neither 373321 nor 374544 equals 373758. Thus, 373758 is not a perfect square.
### d) 22034087
Finally, let's consider 22034087. Estimating the square root gives a value around 4695.86. We check the integers 4695 and 4696:
[tex]\[ 4695 \times 4695 = 22038625 \][/tex]
[tex]\[ 4696 \times 4696 = 22043316 \][/tex]
Neither 22038625 nor 22043316 equals 22034087. Therefore, 22034087 is not a perfect square.
### Summary:
- 1296 is a perfect square.
- 1000 is not a perfect square.
- 373758 is not a perfect square.
- 22034087 is not a perfect square.
So, the numbers 1000, 373758, and 22034087 are not perfect squares.
### a) 1296
First, we find the square root of 1296. The square root of 1296 is found to be 36. We check if squaring 36 gives us back 1296:
[tex]\[ 36 \times 36 = 1296 \][/tex]
Since 1296 equals the square of 36, it confirms that 1296 is a perfect square.
### b) 1000
Next, let's consider 1000. We estimate the square root of 1000 and find it is approximately 31.62. We then check the integers close to this value, which are 31 and 32, to see if squaring either of them results in 1000:
[tex]\[ 31 \times 31 = 961 \][/tex]
[tex]\[ 32 \times 32 = 1024 \][/tex]
Neither 961 nor 1024 equals 1000. Therefore, 1000 is not a perfect square.
### c) 373758
Now, let's look at 373758. Estimating the square root gives a value around 611.28. We check the integers 611 and 612:
[tex]\[ 611 \times 611 = 373321 \][/tex]
[tex]\[ 612 \times 612 = 374544 \][/tex]
Neither 373321 nor 374544 equals 373758. Thus, 373758 is not a perfect square.
### d) 22034087
Finally, let's consider 22034087. Estimating the square root gives a value around 4695.86. We check the integers 4695 and 4696:
[tex]\[ 4695 \times 4695 = 22038625 \][/tex]
[tex]\[ 4696 \times 4696 = 22043316 \][/tex]
Neither 22038625 nor 22043316 equals 22034087. Therefore, 22034087 is not a perfect square.
### Summary:
- 1296 is a perfect square.
- 1000 is not a perfect square.
- 373758 is not a perfect square.
- 22034087 is not a perfect square.
So, the numbers 1000, 373758, and 22034087 are not perfect squares.
