(i) We have,
1 + 3 + 5 + 7 + 9 + 11 + 13
We know that,
Sum of first n odd numbers = n2
Therefore,
1 + 3 + 5 + 7 + 9 + 11 + 13 =(7)2
(ii) By using long division method, we have
Therefore,
\(\sqrt{1681}=41\)
(iii) We know that,
The smallest square number which is exactly divisible by 2, 4 and 6 is 36
Also,
L.C.M of 2, 4b and 6 is 12
Prime factorization of 12 = 2 × 2 × 3
Now, for making it a perfect square we have to multiply it by 3
Therefore,
12 × 3 = 36
(iv) We know that,
A given number is a perfect square having n digits, where n is odd. Then, its square root will have \((\frac{n+1}{2})\) digits