Question

6. Find the smallest whole number by which each of the following numbers should be multiplied, so as to get a perfect square number. Also, find the square root of the number so obtained.
a. 240
b. 375
c. 1,575
d. 1,800​

Answer 1

Step-by-step explanation:

a. 240

= 2×2×2×2×3×5

= (2×2)×(2×2)×3×5

so 240 should be multiplied by 3×5=15 so as to a perfect square number

b. 375

=3×5×5×5

= (5×5) ×3×5

so 375 should be multiplied by 3×5=15 so as to a perfect square number

c. 1,575

= 5×5×3×3×7

= (5×5) ×(3×3) ×7

so 1575 should be multiplied by 7 so as to a perfect square number

d. 1,800

= 2×2×2×3×3×5×5

= (2×2) ×(3×3) ×(5×5) ×2

so 1800 should be multiplied by 2 so as to a perfect square number