Question

4. Students of a class collected 4096 for the
school fete. After the collection, they observed
that the number of students is equal to the
amount contributed by each student. Find the
number of students.
TI​

Answer 1

Let the number of students be x.

Amount contributed by one student = x

A. T. Q.,

x×x=4096

x=√4096

x=64

Answer 2

Answer:

The number of students was $\sf\green { 64}$.

Step-by-step explanation:-

$\sf\blue {Given - }$

• Total amount of contribution collected = ₹4096

• The number of students is equal to the amount contributed by each student.

$\sf\blue {To \: find - }$

• Total number of students in the class.

$\sf\blue {Solution -}$

Let the number of students in the class be = $\sf\green { x }$

Then the contribution by one student will become = $\sf\green { x }$

[ Since we have given the total amount of contribution = the number of students ]

Total amount of contribution contribution was 4096.

A/q we can say that-:

$\sf\red {x \times x = 4096 \: Rs}$

$\sf\red { {x}^{2} = 4096Rs}$

$\sf\red {x = \sqrt{4096}}$

By prime factorization method to get the root of 4096,

[ For prime factorization, refer the attachment ]

we get,

$\sf\green { \sqrt{4096} = \sqrt{\underline {4 \times 4} \times \underline {4 \times 4} \times\underline { 4 \times 4}}}$

$\sf\green {\sqrt{4096} = 4 \times 4 \times 4}$

$\sf\blue { \sqrt{4096} = 64}$

Hence,

$\sf\blue {{x}^{2} = \sqrt{4096} = 64}$

Since, the contribution was equal to the number of students, therefore the result comes that the number of students in the class was $\sf\green { 64.}$

___________________________________