Maharashtra BoardEnglish MediumSTD 8MathsSquares and Square Roots3 Marks
Question
Show that the following numbers is a perfect square. Also, find the number whose square is the given number in case:4761
✓
Answer
In problem, factorise the number into its prime factors.
$4761=3 \times 3 \times 23 \times 23$
Grouping the factors into pairs of equal factors, we obtain,
$4761=(3 \times 3) \times(23 \times 23)$
No factors are left over. Hence, 4761 is a perfect square. The above expression is already grouped into equal factors,
$4761=(3 \times 23) \times(3 \times 23)$
$4761=(3 \times 23)^2$
Hence, 4761 is the square of 69 , which is equal to $3 \times 23$.
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