Question

find the smallest perfect square which is divisibal by 9,10,11 and also and find it's squre root​

Answer 1

Step-by-step explanation:

Question :

find the smallest perfect square which is divisibal by 9,10,11 and also and find it's squre root

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Answer :

★ $\fbox\green{First \: we \: will \: find \: the \: LCM \: of \: 9,10,11.}$

★ $\bf\red{∴LCM \: of \: 9,10 \: and \: 11 = 990}$

Now, we will find out the prime factors of 990.

$\begin{array}{r | l} 2 & 990 \\ 3 & 495 \\ 3 & 165 \\ 5 & 55 \\ {11} & 11 \\ & 1 \end{array}$

Prime factors of 990 = 2 × 3 × 3 × 5 × 11

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As we can see that prime factor 2,5 and 11 has no pair.

Therefore 990 must be multiplied by 2, 5 and 11 to make it a perfect square.

$\blue{∴ 990 × 2 × 5 × 11 = 1,08,900}$

Therefore, the the smallest perfect square which is divisibal by 9,10 and 11 is 108900.

$\bf\red{Square \: root \: of \: 108900 = \sqrt{108900} = 330}$