Question

By what smallest number should 216 be divided so that the quotient is a perfect square . also find the square root of the quotient.

Answer 1

$\mathbb{ SOLUTION }$ :

Prime factors of 216 = 2 × 2 × 2 × 3 × 3 × 3

216 = 2² × 3² × 2 × 3

We find that, there is no prime factor from a pair with 2 and 3

$\therefore$ We must divide the number by 6 so that the quotient becomes a perfect square.

If we divide the given number by 2 × 3 = 6, then

New number = $\frac{ 216}{6}$ = 36

Taking one factor from each, we get square root of new number (quotient)

= 2 × 3 = 6

Answer 2

Hey there !!


▶ Question :-

→ By what smallest number should 216 be divided so that the quotient is a perfect square . Also find the square root of the quotient.


▶ Solution :-

The given number is 216.

The prime factor of 216 = 2 × 2 × 2 × 3 × 3 × 3.

$= \underline{2 \times 2} \times \underline{3 \times 3} \times 2 \times 3.$
The 2 and 3 doesn't make any pair .

So, the product of the these remaining prime factors is the required answer . i.e., 2 × 3 = 6.


$\therefore \frac{216}{6} = 36.$

Therefore, 36 is the perfect square .

$and \: \boxed{ \sqrt{36} = 6.}$



✔✔ Hence, 6 is the smallest number ✅✅.



THANKS



#BeBrainly.