# Ex.6.1 Q7 Squares and Square Roots Solutions - NCERT Maths Class 8

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## Question

(i)

$$1 + 3 + 5 + 7 + 9$$

(ii)

\left[ \begin{align} &1 + 3 + 5 + 7 + 9 + 11 + \\ &13 + 15 + 17 + 19 \\ \end{align} \right]

(iii)

\left[ \begin{align} &1 + 3 + 5 + 7 + 9 + 11 + 13 + \\ &15 + 17 + 19 + 21 + 23 \\ \end{align} \right]

## Text Solution

What is known?

Consecutive odd numbers.

What is uknown?

Sum of these consecutive odd number without adding.

Reasoning:

Sum of the first n odd natural numbers is $$n^2$$ .

Steps:

(i) $$1 + 3 + 5 + 7 + 9$$

Here number of term $$(n)$$ is $$5$$

$${\mathop{\rm Sum}\nolimits} = {(5)^2} = 25$$

(ii)

\left[ \begin{align} &1 + 3 + 5 + 7 + 9 + 11 + \\ &13 + 15 + 17 + 19 \\ \end{align} \right]

Here number of term $$(n)$$ is $$10$$

$${\mathop{\rm Sum}\nolimits} = {(10)^2} = 100$$

(iii)

\left[ \begin{align} &1 + 3 + 5 + 7 + 9 + 11 + 13 + \\ &15 + 17 + 19 + 21 + 23 \\ \end{align} \right]

Here number of term $$(n)$$ is $$12$$

$${\mathop{\rm Sum}\nolimits} = {(12)^2} = 144$$

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