What should come in the place of question mark (?) in the following question?

\(\frac{{7.2}}{{\sqrt[3]{{0.729}}}} = \frac{{{{\left( ? \right)}^3}}}{{{{\left( 2 \right)}^3}}}\)

  1. 4
  2. 5
  3. 6
  4. 8
  5. 9

Answer (Detailed Solution Below)

Option 1 : 4
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IBPS PO 2024 Prelims Full Test 1
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Detailed Solution

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Concept used:

Follow BODMAS rule to solve this question, as per the order given below:

image (4) (1)

\(\frac{{7.2}}{{\sqrt[3]{{0.729}}}} = \frac{{{{\left( ? \right)}^3}}}{{{{\left( 2 \right)}^3}}}\)

\(\Rightarrow \frac{{7.2}}{{\sqrt[3]{{\frac{{729}}{{1000}}}}}} = \frac{{{{\left( ? \right)}^3}}}{{{{\left( 2 \right)}^3}}}\)

\(\Rightarrow \frac{{7.2}}{{\sqrt[3]{{{{\left( {\frac{9}{{10}}} \right)}^3}}}}} = \frac{{{{\left( ? \right)}^3}}}{{{{\left( 2 \right)}^3}}}\)

\(\Rightarrow {\rm{\;}}\frac{{7.2}}{{\sqrt[3]{{{{\left( {0.9} \right)}^3}}}}} = \frac{{{{\left( ? \right)}^3}}}{{{{\left( 2 \right)}^3}}}\)

\(\Rightarrow \frac{{7.2}}{{0.9}} = \frac{{{{\left( ? \right)}^3}}}{{{{\left( 2 \right)}^3}}}\)

⇒ 8 = (?)3/(2)3

⇒ (2)3 = (?)3/(2)3

⇒ 23 × 23 = (?)3

⇒ 43 = (?)3

⇒ ? = 4

∴ The value of ? is 4.
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