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Answer :

Let the number of rows be x and x be the number of plants in each row.

∴we have total number of plants=\(x^2\) = \(\sqrt{2025}\)

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

\(\qquad \begin{array}{c|lcr}
3 & 2025\\
\hline
3 & 675\\
\hline
3 & 225\\
\hline
3 & 75\\
\hline
5 & 25\\
\hline
5 & 5\\
\hline
& 1\\
\end{array}
\)

\(\Rightarrow \sqrt { 3\times 3\times 3\times 3\times 5\times 5 }\)

\(\Rightarrow \sqrt { { 3 }^{ 2 }\times { 3 }^{ 2 }\times { 5 }^{ 2 } }\)

\(\Rightarrow 3 \times 3 \times 5\)

\(\Rightarrow 45\)

Hence, the number of rows is 45 and the number of plants in each row is also 45

- 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
- 7.The students of class VIII of a school donated ₹ 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.
- 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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