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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
Find the square of the given number.
32
Write a Pythagorean triplet whose one member is 6.
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 :
52 + 62 + 72 + 82 + 92 + 102 + 112 + 122
Which of the following number square of even number?
4489
Find the squares of the following numbers using column method. Verify the result by finding the square using the usual multiplication:
37
Find the squares of the following numbers using diagonal method:
98
Find the square of the following number:
512
The sides of a right triangle whose hypotenuse is 17 cm are ______ and ______.
For every natural number m, (2m – 1, 2m2 – 2m, 2m2 – 2m + 1) is a pythagorean triplet.
Rahul walks 12 m north from his house and turns west to walk 35 m to reach his friend’s house. While returning, he walks diagonally from his friend’s house to reach back to his house. What distance did he walk while returning?
