[tex]\begin{gathered} \underline\mathfrak{\purple{Question : -}} \begin{gathered} {} \\ \end{gathered}\end{gathered} [/tex]
❖ Find the smallest perfect square divisible by
2,3 and 5. Also find the square root of the
perfect square.
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Given-
To Find-
Solution-
[tex]\large{\sf{ \implies L.C.M = 2×3×5}}[/tex]
[tex]\large{\sf{ \implies L.C.M = 30}}[/tex]
Square of 30-
[tex]\large{\sf{ \implies 30^{2} }}[/tex]
[tex]\large{\sf{ \implies 30 \times 30 }}[/tex]
[tex]\large{\sf{ \implies 900 }}[/tex]
•°• The number is 900 and the square root of that number is 30.
Verified answer
[tex]\large\underline{\sf{Solution-}}[/tex]
We have to find the smallest perfect square divisible by
2,3 and 5.
So, the smallest number which is divisible by 2, 3 and 5 is LCM of 2, 3 and 5.
So, LCM of 2, 3 and 5 = 2 × 3 × 5 = 30
Now, Prime factorization of 30 = 2 × 3 × 5, and these prime factors are not in pairs. In order to get a perfect square, all these prime factors must occur in pairs.
So, we have to make the pairs of 2, 3 and 5.
So, 30 should be multiplied by 2 × 3 × 5, i.e 30
So, the the smallest perfect square divisible by 2, 3 and 5 is 30 × 30 = 900.
Now,
[tex] \bf \: \sqrt{900} \\ \\ [/tex]
[tex]\sf \: = \: \sqrt{2 \times 2 \times 3 \times 3 \times 5 \times 5} \\ \\ [/tex]
[tex]\sf \: = \: 2 \times 3 \times 5 \\ \\ [/tex]
[tex]\sf \: = \: 30 \\ \\ [/tex]
Hence,
[tex]\bf\implies \: \sqrt{900} = 30 \\ \\ [/tex]