Question

4. Find the smallest number by which each of the following numbers must be multiplied to get a
perfect square number. Also, find the square root of the resulting number:
(ii) 2592
(iii) 3832
(iv) 3380
(I) 588​

Answer 1

(ii) 2592
let's factorise it
factors of 2592: 2×2×2×2×2×9×9
=(2×2)(2×2)(9×9)(2)
so the smallest no by which 2592 should be multiplied to get a perfect square 2.
so the square no is 5184
let's find its square root :

(iii) 3832
let's factorise it
factors : 2×2×2×479
=(2×2)(2)(479)
so the smallest no by which 3832 should be multiplied to get a perfect square is 2*479= 958
so the square no is 3671056
square root of 3671056
(iv) 3380
let's factorise it
factors : 2×2×5×13×13
=(2×2)(13×13)(5)
so the smallest no by which 3380 should be multiplied to get a perfect square is 5
resulted no : 3380×5=16900
square root of 16900=130
(I) 588
let's factorise it
factors : 2×2×3×7×7
=(2×2)(7×7)(3)
so the smallest no by which 588 should be multiplied to get a perfect square is 7
resulted no : 1764
square root of 1764 = 42
Hope it helpful to you and make me brainlist please