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(i) 525

(ii) 1750

(iii) 252

(iv) 1825

(v) 6412

Answer :

(i)

\(\qquad \begin{array}{c|lcr}
&22\\
\hline
2 &\;\; \;\bar{5}\bar{25}\\
&-4\\
\hline
42 &\;\;\; 125\\
&\;\;\; 84\\
\hline
&\;\;\;41\\
\hline
\end{array}
\)

So we got remainder as 41.It represents that the square of 22 is less than 525.So, the next number is 23 and \(23^2 = 529\).

Hence, the number to be added = 529 – 525 = 4

∴Required perfect square = 529

Thus we have, \(\sqrt{529}=23\)

(ii)

\(\qquad \begin{array}{c|lcr}
&41\\
\hline
4 &\;\; \;\bar{17}\bar{50}\\
&-16\\
\hline
81 &\;\;\; 150\\
&\;\;\; 81\\
\hline
&\;\;\;69\\
\hline
\end{array}
\)

So we got remainder as 69.It represents that the square of 41 is less than 1750.So, the next number is 42 and \(42^2 = 1764\).

Hence, the number to be added = 1764– 1750 =14

∴Required perfect square = 1764

Thus we have, \(\sqrt{1764}=42\)

(iii)

\(\qquad \begin{array}{c|lcr}
&15\\
\hline
1 &\;\; \;\bar{2}\bar{52}\\
&-16\\
\hline
25 &\;\;\; 152\\
&\;\;\; 125\\
\hline
&\;\;\;27\\
\hline
\end{array}
\)

So we got remainder as 27.It represents that the square of 15 is less than 252.So, the next number is 16 and \(16^2 = 256\).

Hence, the number to be added = 256 – 252 = 4

∴Required perfect square = 256

Thus we have, \(\sqrt{256}=16\)

(iv)

\(\qquad \begin{array}{c|lcr}
&42\\
\hline
4 &\;\; \;\bar{18}\bar{25}\\
&-16\\
\hline
82 &\;\;\; 225\\
&\;\;\; 164\\
\hline
&\;\;\;61\\
\hline
\end{array}
\)

So we got remainder as 61.It represents that the square of 42 is less than 1825.So, the next number is 43 and \(43^2 = 1849\).

Hence, the number to be added = 1849 – 1825 = 24

∴New number = 1849

Thus we have,\(\sqrt{1849}=43\)

(v)

\(\qquad \begin{array}{c|lcr}
&80\\
\hline
8 &\;\; \;\bar{64}\bar{12}\\
&-64\\
\hline
160 &\;\;\; 12\\
&\;\;\; 0\\
\hline
&\;\;\;12\\
\hline
\end{array}
\)

So we got remainder as 12.It represents that the square of 80 is less than 6412.So, the next number is 81 and \(81^2 = 6561\).

Hence, the number to be added = 6561 – 6412 = 149

∴New number = 6561

Thus, we have \(\sqrt{6561}=81\)

- 1.Find the square root of each of the following numbers by Long Division method. (i) 2304 (ii) 4489 (iii) 3481 (iv) 529 (v) 3249 (vi) 1369 (vii) 5776 (viii) 7921 (ix) 576 (x) 1024 (xi) 3136 (xii) 900
- 2.Find the number of digits in the square root of each of the following numbers (without any calculation) (i) 64 (ii) 144 (iii) 4489 (iv) 27225 (v) 390625
- 3.Find the square root of the following decimal numbers. (i) 2.56 (ii) 7.29 (iii) 51.84 (iv) 42.25 (v) 31.36
- 4.Find the least number which must be subtracted from each of the following numbers so as to get a perfect square. Also find the square root of the perfect square so obtained. (i) 402 (ii) 1989 (iii) 3250 (iv) 825 (v) 4000
- 6.Find the length of the side of a square whose area is \(441 m^2\)
- 7.In a right triangle ABC, ∠B =\( 90^{\circ}\). (a) If AB = 6 cm, BC = 8 cm, find AC (b) If AC = 13 cm, BC = 5 cm, find AB
- 8.A gardener has 1000 plants. He wants to plant these in such a way that the number of rows and the number of columns remain the same. Find the minimum number of plants he needs more for this.
- 9.There are 500 children in a school. For a P.T. drill, they have to stand in such a manner that the number of rows is equal to the number of columns. How many children would be left out in this arrangement?

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