Ex.6.1 Q4 Squares and Square Roots Solutions - NCERT Maths Class 8

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Question

Observe the following pattern and find the missing digits.

\[\begin{align}{11^2} &= 121\\{101^2} &= 10201\\{1001^2} &= 1002001\\{100001^2} &= 1 \ldots .2....1\\{10000001^2} &= \ldots ..........\end{align}\]

Text Solution

What is known?

Pattern

What is uknown?

Missing number in the pattern

Reasoning:

The square of the given number has the same number of zeros before and after the digit \(2\) as it has in the original number.

Steps:

\[\begin{align}{11^2} &= 121\\{101^2} &= 10201\\{1001^2}& = 1002001\\{100001^2} &= 10000200001\\{10000001^2}& = 100000020000001\end{align}\]