Ex.6.4 Q2 Squares and Square Roots - NCERT Maths Class 8

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Question

Find the number of digits in the square root of each of the following numbers (without any calculation).

(i) $$64$$

(ii) $$144$$

(iii) $$4489$$

(iv) $$27225$$

(v) $$390625$$

Text Solution

What is known?

Squares

What is unknown?

Number of digits in square root

Reasoning:

If a perfect square is of n digits then it’s square root will have \begin{align}\frac{n}{2}\end{align} digits, if n is even and \begin{align}\frac{{\left( {n + 1} \right)}}{2}\end{align} if $$n$$ is odd

Steps

(i) $$64$$

$$n = 2 \rm(even)$$

\begin{align}{\rm{Number}}\;{\rm{of}}\;{\rm{digits}} = \frac{2}{2} = 1\end{align}

(ii) $$144$$

$$n = 3$$

\begin{align}{\rm{Number}}\;{\rm{of}}\;{\rm{digits}} &= \frac{{n + 1}}{2}\\ &= \frac{{3 + 1}}{2} \\&= \frac{4}{2} = 2\end{align}

(iii) $$4489$$

$$n = 4$$

\begin{align}{\rm{Number}}\;{\rm{of}}\;{\rm{digits}} = \frac{n}{2} = \frac{4}{2} = 2\end{align}

(iv) $$27225$$

$$n = 5$$

\begin{align}{\rm{Number}}\;{\rm{of}}\;{\rm{digits}} &= \frac{{n + 1}}{2}\\ &= \frac{{5 + 1}}{2} \\&= \frac{6}{2} = 3\end{align}

(v) $$390625$$

$$n = 6$$

\begin{align}{\rm{Number}}\;{\rm{of}}\;{\rm{digits}} = \frac{n}{2} = \frac{6}{2} = 3\end{align}

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