Q. 134.0( 6 Votes )

# Fill in the blanks:

(i) 1+3 +5 +7+9 +11+13 =(…….)^{2}

(ii) = ……….

(iii) The smallest square number exactly divisible by 2, 4, 6 is

(iv) A given number is a perfect square having n digits, where n is odd. Then, its square root will have …………… digits.

Answer :

(i) We have,

1 + 3 + 5 + 7 + 9 + 11 + 13

We know that,

Sum of first n odd numbers = n^{2}

Therefore,

1 + 3 + 5 + 7 + 9 + 11 + 13 = **(7) ^{2}**

(ii) By using long division method, we have

Therefore,

= **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 **(****)** digits

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