Ex.6.1 Q8 Squares and Square Roots Solutions - NCERT Maths Class 8

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Question

(i)  Express \(49\) as the sum of \(7\) odd numbers.

(ii) Express \(121\) as the sum of \(11\) odd numbers.

Text Solution

What is known?

Sum of \(7\) odd number is \(49\)

Sum of \(11\) odd number is \(121\)

What is uknown?

Express \(49\) as the sum of \(7 \) odd numbers and \(121\) as the sum of 11 odd numbers.

Reasoning:

The sum of successive odd natural numbers is \(n^2\).

Steps:

(i) \(49 = {\left( 7 \right)^2}\)

Therefore ,\(49\) is the sum of first \(7\) odd natural numbers

\(49 = 1 + 3 + 5 + 7 + 9 + 11 + 13\)

(ii) \(121={\left(11 \right)^2}\)

Therefore ,\(121\) is the sum of first \(11\) odd natural numbers

\(121 = \left[ \begin{array}{l}  1  +  3  +  5  +  7  +  9  +  11  +   \\13  +  15  +  17  +  19  +  21 \\ \end{array} \right]\)