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in Squares And Square Roots by (30.8k points)
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Fill in the blanks:

(i) 1+3 +5 +7+9 +11+13 =(…….)2

(ii) \(\sqrt{1681}\) = ……….

(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.

1 Answer

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by (31.2k points)
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Best answer

(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

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