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प्रश्न
Which of the following number is squares of even number ?
256
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उत्तर
The numbers whose last digit is odd can never be the square of even numbers.
For each number, use prime factorisation method and make pairs of equal factors.
256 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2
= (2 x 2) x (2 x 2) x (2 x 2) x (2 x 2)
There are no factors that are not paired. Hence, 256 is a perfect square. The square of an even number is always even. Hence, 256 is the square of an even number.
संबंधित प्रश्न
What will be the units digit of the square of the following number?
52
What will be the units digit of the square of the following number?
12796
From the pattern, we can say that the sum of the first n positive odd numbers is equal to the square of the n-th positive number. Putting that into formula:
1 + 3 + 5 + 7 + ... n = n2, where the left hand side consists of n terms.
Observe the following pattern \[1^2 = \frac{1}{6}\left[ 1 \times \left( 1 + 1 \right) \times \left( 2 \times 1 + 1 \right) \right]\]
\[ 1^2 + 2^2 = \frac{1}{6}\left[ 2 \times \left( 2 + 1 \right) \times \left( 2 \times 2 + 1 \right) \right]\]
\[ 1^2 + 2^2 + 3^2 = \frac{1}{6}\left[ 3 \times \left( 3 + 1 \right) \times \left( 2 \times 3 + 1 \right) \right]\]
\[ 1^2 + 2^2 + 3^2 + 4^2 = \frac{1}{6}\left[ 4 \times \left( 4 + 1 \right) \times \left( 2 \times 4 + 1 \right) \right]\] and find the values :
12 + 22 + 32 + 42 + ... + 102
Which of the following number are square of even number?
6561
Which of the following number square of even number?
373758
Find the square of the following number:
451
For every natural number m, (2m – 1, 2m2 – 2m, 2m2 – 2m + 1) is a pythagorean triplet.
Find the area of a square field if its perimeter is 96 m.
Put three different numbers in the circles so that when you add the numbers at the end of each line you always get a perfect square.
