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Real Numbers
RD Sharma Ch 01
CBSE_RD_SHARMA_CH01
Grade 10

Question:

The prime factorisation of $3825$ is:

$3 \times 5^2 \times 17$
$3^2 \times 5^2 \times 17$
$3^3 \times 5 \times 17$
$3^2 \times 5^3 \times 17$

Step-by-Step Solution

Key Concept: Divide continuously by prime factors: $3825 = 9 \times 25 \times 17 = 3^2 \times 5^2 \times 17$.
Stepwise Solution:

$3825 / 3 = 1275 / 3 = 425 / 5 = 85 / 5 = 17 / 17 = 1$. [0.5 Mark]

$3825 = 3^2 \times 5^2 \times 17$. [0.5 Mark]

Marking Scheme:

• Prime factorisation steps: 0.5 Mark
• Selecting correct canonical form: 0.5 Mark

Correct Answer: $3^2 \times 5^2 \times 17$
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