Question

By what number should each of the following numbers be multiplied to get a perfect square in each case ? Also, find the number whose square is the new number.
(i) 8820 (ii) 3675 (iii) 605 (iv) 2880 (v) 4056 (vi) 3468 (vii) 7776

Answer 1

(i) $8820=2\times 2\times 3\times 3\times 5\times 7\times 7$

Grouping the factors in pairs, we see that are 5 is left unpaired
$\therefore$ By multiplying 8820 by 5, we got the perfect sqaure and square root of product will be $=2\times 3\times 5\times 7=210$

(ii) $3675=3\times 5\times 5\times 7\times 7$

Grouping the factors in pairs, we see that are 3 are left unpaired
$\therefore$ Multiplying 3675 by 3, we get a perfect square and square of the product will be = $3\times 5\times 7=105$

(iii) $605=5\times 11\times 11$

Grouping the factors in pairs, we see that are 3 and 7 are left unpaired
$\therefore$ Multiplying 605 by 5, we got a perfect sqaure and sqaure root of the product will be $=5\times 11=55$

(iv) $2880=2\times 2\times 2\times 2\times 2\times 2\times 3\times 3\times 5$

Grouping the factors in pairs, we see that are 5 is left unpaired
$\therefore$ Multiplying 2880 by 5, we got the perfect sqaure.
Square root of product will be $2\times 2\times 2\times 3\times 5=120$

(v) $4056=2\times 2\times 2\times 3\times 13\times 13$

Grouping the factors in pairs, we see that 2 and 3 are left unpaired
$\therefore$ Multiplying 4056 by $2\times 3$ i.e., 6, we get that perfect square.
and square root of he product will be $=2\times 2\times 3\times 13=156$

(vi) $3468=2\times 2\times 3\times 17\times 17$

Grouping the factors in pairs, we see that is left unpaired
$\therefore$ Multiplying 3468 by 3 we get a perfect square and square root of the product will be $2\times 3\times 17=102$

(vii)7776= $2\times 2\times 2\times 2\times 2\times 3\times 3\times 3\times 3\times 3$

Grouping the factors in pairs, we se that 2 and 3 are left unpaired
$\therefore$ Multiplying 7776 by $2\times 3$ or 6
We get a perfect square
and square root of the product will be $=2\times 2\times 2\times 3\times 3\times 3\times =216$