Question
Show that the following numbers is a perfect square. Also, find the number whose square is the given number in each case: $1156$
✓
Answer
In problem, factorise the number into its prime factors.
$1156 = 2 \times 2 \times 17 \times 17$
Grouping the factors into pairs of equal factors, we obtain,
$1156 = (2 \times 2) \times (17 \times 17)$
No factors are left over. Hence, 1156 is a perfect square. Moreover, by grouping 1156 into equal factors,
$1156 = (2 \times 17) \times (2 \times 17)$
$1156 = (2 \times 17)^2$
Hence, 1156 is the square of 34, which is equal to $2 \times 17$
$1156 = 2 \times 2 \times 17 \times 17$
Grouping the factors into pairs of equal factors, we obtain,
$1156 = (2 \times 2) \times (17 \times 17)$
No factors are left over. Hence, 1156 is a perfect square. Moreover, by grouping 1156 into equal factors,
$1156 = (2 \times 17) \times (2 \times 17)$
$1156 = (2 \times 17)^2$
Hence, 1156 is the square of 34, which is equal to $2 \times 17$
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