Question

Show that each of the following numbers is a perfect square. Also, find the number whose square is the given number in each case:
(i) 1156 (ii) 2025
(iii) 14641 (iv) 4761

Answer 1

(i) 1156 = $2\times 2\times 17\times 17$

Grouping the factors in pairs, we see that factor is left unpaired
$\therefore$ 1156 is a perfect square of $2\times 17=34$

(ii) $2025=3\times 3\times 3\times 3\times 3\times 5\times 5$

Grouping the factors in pairs, we see that factor is left unpaired
$\therefore$ 2025 is a perfect square of $3\times 3\times 5=45$

(iii) $14641=11\times 11\times 11\times 11$

Grouping the factors in pairs, we see that factor is left unpaired
$\therefore$ 1461 is a perfect square of $11\times 11=121$

(iv) $4761=3\times 3\times 23\times 23$

Grouping the factors in pairs, we see that factor is left unpaired
$\therefore$ 4761 is a perfect square of $3\times 23=69$