Ex.6.3 Q9 Squares and Square Roots Solutions - NCERT Maths Class 8

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Question

Find the smallest square number that is divisible by each of the numbers \(4\),\( 9\) and \(10\).

Text Solution

What is known?

Divisor are 4, 9 and 10

What is unknown?

The smallest square that is divisible by 4, 9 and 10.

Reasoning:

The number that will be perfectly divisible by each one of the numbers is their \(LCM\).

Steps:

\[\begin{align}&2\left| \!{\underline {\,{4,9,10} \,}} \right. \\&2\left| \!{\underline {\,{2,9,5} \,}} \right. \\&3\left| \!{\underline {\,{1,9,5} \,}} \right. \\&3\left| \!{\underline {\,{1,3,5} \,}} \right. \\&5\left| \!{\underline {\,{1,1,5} \,}} \right. \\&1\left| \!{\underline {\,{1,1,1} \,}} \right. \end{align}\]

\(LCM\) of \(4,9,10\)
\[\begin{align}& =\text{ }2\times ~2\times 3\times 3~\times 5 \\& =\text{ }180 \\
\end{align}\]

Hence, number \(5\) does not have a pair. Therefore \(180\) is multiplied by \(5\) then the number obtained is a perfect square. Therefore, \(180~\times 5\text{ }=\text{ }900\)

So, \(900\) is the smallest square that is divisible by \(4\), \(9\) and \(10\).