
List all the perfect squares between and . Which of these numbers form a Pythagorean triplet? How many triplets can you find?
Answer
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Hint: As we know that a perfect square is a number that can be expressed as the square of a number from the number system. For example, is a perfect square. It is the square of the natural number i.e. . Now by applying this we will write all the perfect squares between and .
Complete step-by-step answer:
We have to find the perfect squares between and .
By applying the above definition we have the perfect squares .
So there are total perfect squares between and .
Now we know that a Pythagorean triplet consists of three positive terms and , such that .
We can write these perfect squares as .
From the above we have to choose three numbers such that .
We can see that there is only one such pair that forms the Pythagorean triplet which is .
It can be written as . On further solving by squaring we have .
Hence the required Pythagorean triplet is .
So, the correct answer is “ ”.
Note: We should note that is the most known and smallest Pythagorean triplet. We should know that if a triangle has one angle which is right angle i.e. , then there is the Pythagoras theorem. Let us take to be the hypotenuse and the other two sides are and , then it states that . We can define it as the sum of the squares of the other two sides is the same as the square of the longest side.
Complete step-by-step answer:
We have to find the perfect squares between
By applying the above definition we have the perfect squares
So there are total
Now we know that a Pythagorean triplet consists of three positive terms
We can write these perfect squares
From the above we have to choose three numbers such that
We can see that there is only one such pair that forms the Pythagorean triplet which is
It can be written as
Hence the required Pythagorean triplet is
So, the correct answer is “
Note: We should note that
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