# Ex.6.3 Q7 Squares and Square Roots Solutions - NCERT Maths Class 8

## Question

The students of Class \(VIII\) of a school donated \(\rm Rs. 2401\) in all for the Prime Minister’s National Relief Fund. Each student donated as many rupees as the number of students in the class. Find the number of students in the class.

## Text Solution

**What is Known?**

Total amount of donation donated by students.

**What is Unknown?**

Number of students in the class.

**Reasoning:**

Each student donated as many rupees as the number of students in the class i.e. money donated by each student is equal to the number of students in the class. Total amount of donation is equal to the product of number of students in the class and money donated by each student.

**Steps:**

Let number of students in a class be \(x\)

So, money donated by each student is also \(x\) (as they donated as much amount as number of students in the class).

Total amount of donation \(= \rm Rs \,2401\)

Total amount of donation \( = \) number of students \( \times \)money donated by each student

\[\begin{align}2401 &= x \times x\\2401 &= {x^2}\\x &= \sqrt {2401} \end{align}\]

\[\begin{align}&7\left| \!{\underline {\,{2401} \,}} \right. \\&7\left| \!{\underline {\,{343} \,}} \right. \\&7\left| \!{\underline {\,{49} \,}} \right. \\&7\left| \!{\underline {\,7 \,}} \right. \\&1\left| \!{\underline {\,1 \,}} \right. \end{align}\]

\[\begin{align}&x = \sqrt {2401} \\&x = \sqrt {7 \times 7 \times 7 \times 7} \\&x = \sqrt {{7^2} \times {7^2}} \\&x = \sqrt {{{(7 \times 7)}^2}} \\&x = 7 \times 7 = 49\end{align}\]

Therefore, the number of students in class is \(49\).