Question

12. The least possible value of A for which 90 A is
a perfect cube is
(a) 200
(b) 300
(c) 500
(d) 600


answered me plz​

Answer 1

$\: \: \boxed{\boxed{\bf{\mapsto \: \: \: Question}}}$

The least possible value of A for which 90 A is a perfect cube is

(a) 200

(b) 300

(c) 500

(d) 600

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$\: \: \boxed{\boxed{\bf{\mapsto \: \: \: Answer}}}$

The least possible value of A for which 90 A is a perfect cube is 300 .

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$\: \: \boxed{\boxed{\bf{\mapsto \: \: \: Solution}}}$

To find ,

» least possible value of A

Given ,

» 90 × A

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Let's factorise 90 ,

⠀2 | 90⠀

⠀3 | 45⠀

⠀3 | 15⠀

⠀5 | 5⠀

⠀⠀| 1⠀

Now on factorising 90 we get = 2 × 5 × 3 × 3

Therefore , least value of A for which the given number is a perfect cube

$\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\\\;\large{ \longrightarrow{\sf \underline{3} \times\underline{2 \times 2} \times \underline{5 \times 5} }}\end{gathered}\end{gathered} \end{gathered}\end{gathered} \end{gathered} \end{gathered}\end{gathered} \end{gathered}$

$\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\\\;\large{ \longrightarrow{\sf {3} \times{2 ^{2} } \times {5 ^{2} } }}\end{gathered}\end{gathered} \end{gathered}\end{gathered} \end{gathered} \end{gathered}\end{gathered} \end{gathered}$

$\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\\\;\large{ \longrightarrow{\sf {3} \times{4} \times {25} }}\end{gathered}\end{gathered} \end{gathered}\end{gathered} \end{gathered} \end{gathered}\end{gathered} \end{gathered}$

$\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\\\;\large{ \longrightarrow{\sf \blue{ 300} }}\end{gathered}\end{gathered} \end{gathered}\end{gathered} \end{gathered} \end{gathered}\end{gathered} \end{gathered}$

$\: \: \boxed{\boxed{\bf{\mapsto \: \: \: hence , least\; possible \;value\; of \;A = \underline{300}}}}$