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प्रश्न
Which of the following number square of even number?
324
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उत्तर
The numbers whose last digit is odd can never be the square of even numbers use prime factorisation method and make pairs of equal factors.
324 = 2 x 2 x 3 x 3 x 3 x 3
= (2 x 2) x (3 x 3) x (3 x 3)
There are no factors that are not paired. Hence, 324 is a perfect square. The square of an even number is always even. Hence, 324 is the square of an even number.
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संबंधित प्रश्न
Write a Pythagorean triplet whose one member is 14.
What will be the units digit of the square of the following number?
52
Which of the following triplets are pythagorean?
(8, 15, 17)
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
For every natural number m, (2m – 1, 2m2 – 2m, 2m2 – 2m + 1) is a pythagorean triplet.
If x and y are integers such that x2 > y2, then x3 > y3.
Find the length of the side of a square if the length of its diagonal is 10 cm.
The dimensions of a rectangular field are 80 m and 18 m. Find the length of its diagonal.
Find the area of a square field if its perimeter is 96 m.
