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Answer :

Let x be the number of students in the class. Therefore, total money donated by students:\(x \times x=₹ x^2\)

Here we have, \(x^2 =2401\)

\(\Rightarrow x=\sqrt{2401}\)

\(\qquad \begin{array}{c|lcr}
7 & 2401\\
\hline
7 & 343\\
\hline
7 & 49\\
\hline
7 & 7\\
\hline
& 1\\
\end{array}
\)

\(\Rightarrow x=\sqrt{7 \times 7 \times 7 \times 7}\)

\(\Rightarrow x=7 \times 7 \)

\(\Rightarrow x=49\)

Hence, the number of the students in the class is 49.

- 1.What could be the possible ‘one’s’ digits of the square root of each of the following numbers? (i) 9801 (ii) 99856 (iii) 998001 (iv) 657666025
- 2.Without doing any calculation, find the numbers which are surely not perfect squares. (i) 153 (ii) 257 (iii) 408 (iv) 441
- 3.Find the square roots of 100 and 169 by the method of repeated subtraction.
- 4.Find the square roots of the following numbers by the prime factorisation Method. (i) 729 (ii) 400 (iii) 1764 (iv) 4096 (v) 7744 (vi) 9604 (vii) 5929 (viii) 9216 (ix) 529 (x) 8100
- 5.For each of the following numbers, find the smallest whole number by which it should be multiplied so as to get a perfect square number. Also, find the square root of the square number so obtained. (i) 252 (ii) 180 (iii) 1008 (iv) 2028 (v) 1458 (vi) 768
- 6.For each of the following numbers, find the smallest whole number by which it should be divided so as to get a perfect square. Also, find the square root of the square number so obtained. (i) 252 (ii) 2925 (iii) 396 (iv) 2645 (v) 2800 (vi) 1620
- 8.2025 plants are to be planted in a garden in such a way that each row contains as many plants as the number of rows. Find the number of rows and the number of plants in each row.
- 9.Find the smallest square number that is divisible by each of the numbers 4, 9 and 10.
- 10.Find the smallest number that is divisible by each of the numbers 8, 15 and 20.

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- NCERT solutions for class 8 maths chapter 12 Exponents and Powers
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- NCERT solutions for class 8 maths chapter 14 Factorization
- NCERT solutions for class 8 maths chapter 15 Introduction to Graphs
- NCERT solutions for class 8 maths chapter 16 Playing with Numbers

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