Ch 6 covers perfect squares, their properties, patterns, and methods to find square roots. Students learn prime factorisation and long division methods, and the connection to Pythagorean triplets.
A perfect square is the square of a natural number. Properties: perfect squares end only in 0, 1, 4, 5, 6, or 9 (never 2, 3, 7, 8). The number of zeros at the end is always even. Between n² and (n+1)², there are 2n non-perfect square numbers.
Prime factorisation: factorise the number, pair up identical primes, take one from each pair and multiply. Long division method: group digits in pairs from right, find largest digit whose square fits, continue with subsequent pairs.
For any natural number m > 1, the triplet (2m, m²−1, m²+1) is always a Pythagorean triplet: (2m)² + (m²−1)² = (m²+1)².
Download: https://ncert.nic.in/textbook/pdf/hemh106.pdf | Complete book: https://ncert.nic.in/textbook/pdf/hemh1ps.zip
If a number ends in 2, 3, 7, or 8, it cannot be a perfect square. Also, if the number of trailing zeros is odd, it is not a perfect square.
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