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

Answer:

i.)3

ii.)2

iii.) 958

iv.) 15

Step-by-step explanation:

Find prime factors of all the numbers

i) (2*2) (7*7) (3)

For making square 3 should be multiplied because one 3 is less in the above pair

II.) (2*2) (2*2) (3*3) (2)

For making square 2 should be multiplied because one 2 is less in the above pair

iii.)) (2*2) (2) (479)

For making square 958 should be multiplied because one 2 and 479 and is less in the above pair thus their product should be multiplied

iv) (2*2) (5) (3) (13*13)

For making square 15 should be multiplied because one 5 and 3 and is less in the above pair thus their product should be multiplied

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Answer 2

(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 :

$\sqrt{5184 } = 72$

(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