Question

find the smallest number by which 9072
must be multiplied to get a perfect
square. Also find root of the perfect square
so obtained​

Answer 1

Answer: Smallest number=7

               Root=252

Step-by-step explanation:

To solve this, we have to keep dividing the number [9072] by its prime factors until we get 1 as an answer.

A Prime factor is a number that is divisible only by one and by the number itself. Examples; 2, 3, 5, 7, e.t.c

The Process begins:

We start dividing by the smallest prime number that can divide 9072 first which is 2:

9072 ÷ 2=4536

4536 ÷ 2=2268

2268 ÷ 2=1134

1134  ÷  2=567

567   ÷  3=189

189   ÷   3=63

63    ÷   3=21

21     ÷   3=7

7      ÷    7=1

The prime factors are: 2×2×2×2×3×3×3×3×7

We observe that by grouping the prime factors into twos, we get:

(2×2)×(2×2)×(3×3)×(3×3)×(7×_).

There is no pair for 7, therefore, 7 is the smallest number to which 9072 must be multiplied to get a perfect square.

Hence, the perfect square will be:

=9072 × 7

=63504.

To find its root,

Its prime factors are; (2×2)×(2×2)×(3×3)×(3×3)×(7×7).

So, we take each pair as one number( the number contained in the pair{i.e the pair [2 × 2] will be taken as 2})

So, the root is

=2×2×3×3×7

=252

To check, use a calculator:

$\sqrt{63504}$=252

Answer 2

Step-by-step explanation:

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