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
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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
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