Question

Find the smallest number by which 7776 is to be divided to get a perfect square.​

Answer 1

To Find :-

• smallest number by which 7776 is to be divided to get a perfect square. ?

Solution :-

Prime Factors of 7776 are :-

→ 7776 = 2x2x2x2x2×3x3x3x3x3.

→ 7776 = (2x2)x(2x2)x2×(3x3)x(3x3)x3.

we know That, for a number to be perfect Square we have pair of Two.

So,

→ we can see that, 2 and 3 are not in pair.

Hence,

→ if we Remove Them , we will get a perfect square.

So,

→ smallest number by which 7776 is to be divided to get a perfect square = 2 × 3 = 6 (Ans).

And, Than,

→ it will be square of = 2 × 2 × 3 × 3 = 36 ...

Answer 2

$\huge\bold\green{\underline{SoluTion:}}$

We have considered number=7776

$\bold\green{\underline{Find: Perfect\: square:}}$

At first we have to find out the factors of 7776 by prime factorisation method.

$\bold\green{\underline{Factors\:of\:7776:}}$

=2×2×2×2×2×3×3×3×3×3

Now, making pairs of factors here

(2×2)(2×2)×2(3×3)(3×3)×3

Here we have to notice that out of making pairs which is missing, so pairs of 2 and 3 is missing here

so,product of missing pairs=2×3=6

Hence,the smallest number is 6 which is divided by 6 into 7776 than it becomes perfect quare

$\bold\red{\underline{Verification:}}$

=7776÷6

=1296

Hence ,1296 is perfect quare of 36