Exercise 3 (B)
Q1 | Ex-3B | Square and Square Roots | Class 8 | Schand Composite
Mathematics | myhelper
Find the square root of each of the following numbers by division
method.
(i) 3249
Sol :
$\begin{array}{r|l} &57 \\\hline5&3249\\5&25\\\hline 107
& ~~749 \\ 7&~~749\\\hline &~~~~0 \end{array}$
(ii) 6889
Sol :
$\begin{array}{r|l} &83 \\\hline 8&6889\\8&64\\\hline 163 &
~~489 \\ 3&~~489\\\hline &~~~~0 \end{array}$
(iii) 15129
Sol :
$\begin{array}{r|l} &123 \\\hline 1&15129\\1&1\\\hline 22 &
~~51 \\ 2&~~44\\\hline 243&~~~~~~729\\&~~~~~~729\\ \hline
&~~~~~~~~0 \end{array}$
(iv) 75625
Sol :
$\begin{array}{r|l} &275 \\\hline 2&75625\\2&4\\\hline 47 &
356 \\7&329\\\hline 545&~~2725\\5&~~2725\\ \hline &~~~~~0
\end{array}$
(v) 166464
Sol :
$\begin{array}{r|l} &408 \\\hline 4&166464\\4&16\\\hline 80 &
~~~~64 \\0&~~~~00\\\hline 808&~~6464\\8&~~6464\\ \hline
&~~~~~0 \end{array}$
(vi) 9548100
Sol :
$\begin{array}{r|l} &3090 \\\hline 3&9548100\\3&9\\\hline 60 &
~~54 \\0&~~00\\\hline 609&~~5481\\9&~~5481\\ \hline &~~~~~0
\end{array}$
(vii) \( \dfrac{1089}{3481} \)
Sol :
$=\frac{\sqrt{1089}}{\sqrt{3481}}$
$\begin{array}{r|l} &33 \\\hline 3&1089\\3&9\\\hline 63 &
189 \\3&189\\\hline &~~0 \end{array}$
$\begin{array}{r|l} &59 \\\hline 5&3481\\5&25\\\hline 109 &
~~981 \\9&~~981\\\hline &~~0 \end{array}$
$=\frac{33}{59}$
(viii) \( \dfrac{7569}{14884} \)
Sol :
$=\frac{\sqrt{7569}}{\sqrt{14884}}$
$\begin{array}{r|l} &87 \\\hline 8&7569\\8&64\\\hline 167&
1169 \\17&1169\\\hline &~~0 \end{array}$
$\begin{array}{r|l} &122 \\\hline 1&14884\\1&1\\\hline 22&
~~48 \\2&~~44\\\hline &~~~~484\\&~~~~484\\ \hline &~~~~~~0
\end{array}$
$=\frac{87}{122}$
(ix) \( 2\dfrac{337}{9216} \)
Sol :
$=\sqrt{\left(\frac{9216 \times 2+337}{9216}\right)}$
$=\sqrt{\frac{18769}{9216}}$
$=\frac{\sqrt{18769}}{{\sqrt{9216}}}$
$\begin{array}{r|l} &137 \\\hline 1&18769\\1&1\\\hline 23&
~~87 \\3&~~69\\\hline 267&~~1869\\7&~~1869\\\hline& ~~~~0
\end{array}$
$\begin{array}{r|l} &96 \\\hline 9&9216\\9&81\\\hline 186&
~~1116 \\6&~~1116\\\hline &~~~~0 \end{array}$
$=\frac{137}{96}=1\frac{41}{96}$
(x) \( 9\dfrac{4185}{5776} \)
Sol :
$=\sqrt{\frac{5776 \times 9+4185}{5776}}$
$=\sqrt{\frac{56169}{5776}}$
$=\frac{\sqrt{56169}}{\sqrt{5176}}$
$\begin{array}{r|l} &237 \\\hline 2&56169\\1&4\\\hline 43& 161
\\3&129\\\hline 467&~~3269\\7&~~3269\\\hline& ~~~~0
\end{array}$
$\begin{array}{r|l} &76\\\hline 7&5776\\7&49\\\hline 146&
876\\6&876\\\hline &~~0 \end{array}$
$=\frac{237}{76}$
Q2 | Ex-3B | Square and Square Roots | Class 8 | Schand Composite Mathematics | myhelper
Question 2
Find the perimeter of a square field whose area is 13689
m2
Sol :
Perimeter of square= 4×side
Area of square=side×side=side2
13689=side2
side=$\sqrt{13689}$
$\begin{array}{r|l} &117 \\\hline 1&13689\\1&1\\\hline 21&
~~36 \\1&~~21\\\hline 227&~~1589\\7&~~1589\\\hline& ~~~~0
\end{array}$
side=117
Perimeter of square=4×117=468
Q3 | Ex-3B | Square and Square Roots | Class 8 | Schand Composite Mathematics | myhelper
Question 3
What should be subtracted from 18246 to get a perfect square number ?
What is this perfect square number ? Also, find its square root.
Sol :
$\begin{array}{r|l} &135 \\\hline 1&18246\\1&1\\\hline 23&
~~82 \\3&~~69\\\hline 265&~~1346\\5&~~1325\\\hline& ~~~~~~21
\end{array}$
As it can be seen that square of 135 is less than by 21 (remainder)
If we subtract the remainder 21 from the number 18.246, we get a perfect
square.
∴Required perfect square=18246-21=18.225
Square root$=\sqrt{18225}=135$
Q4 | Ex-3B | Square and Square Roots | Class 8 | Schand Composite Mathematics | myhelper
Question 4
What should be added to 14841 to make the sum a perfect square ?
Sol :
$\begin{array}{r|l} &121 \\\hline 1&14841\\1&1\\\hline 22&
~~48 \\2&~~44\\\hline 241&~~441\\1&~~241\\\hline& ~~~~~~200
\end{array}$
We observe that the given number is greater than square of 121 and less than
square of 122.
So, number to be added$=(122)^{2}-14841$
=14884-14841=43
Resulting number=14841+43=14884
Q5 | Ex-3B | Square and Square Roots | Class 8 | Schand Composite Mathematics | myhelper
Question 5
Find the least number which must be subtracted from 63520 to make it a
perfect square.
Sol :
$\begin{array}{r|l} &252 \\\hline 2&63520\\2&4\\\hline 45&
235 \\5&225\\\hline 502&~~1020\\&~~1004\\ \hline &~~~~~~16
\end{array}$
As it can be seen that square of 252 is less than 63520 by 16 (remainder)
To make it a perfect square, we have to subtract=63520-16=63504
Q6 | Ex-3B | Square and Square Roots | Class 8 | Schand Composite Mathematics | myhelper
Question 6
Find:
(i) Find the least number of six digits which is a perfect
square.
Sol :
The least six digit number is 100000
$\begin{array}{r|l} &316 \\\hline 3&100000\\3&9\\\hline 61&
100 \\1&~~61\\\hline 626&~~3900\\&~~3756\\ \hline &~~~~144
\end{array}$
We can see that square of 316 is less than 100000 by 144
Perfect square=100000-144
=99856=$(316)^2$
But it is not a six digit number.
So, we have to choose next one
$=(317)^2$
=100489
(ii) Find the greatest number of six digits which is a perfect
square.
Sol :
The greatest six digit number is 999999
$\begin{array}{r|l} &999 \\\hline 9&999999\\9&81\\\hline
189& 1899 \\9&1701\\\hline 1989&~~19899\\9&~~17901\\ \hline
&~~~~1998 \end{array}$
We can see that square of 999 is less than 999999 by 1998
∴Required perfect square=999999-1998
=998001
Q7 | Ex-3B | Square and Square Roots | Class 8 | Schand Composite Mathematics | myhelper
Question 7
A gardener arranges his plants in rows to form a perfect square. He finds
that in doing so, 25 plants are left out.If the total number of plants be
2234 , find the numbers of plants in each row.
Sol :
Prefect square number=Total plants-Left out plants
=2234-25=2209
Number of plants in each row
$=\sqrt{2209}$
=47
$\begin{array}{r|l} &47 \\\hline 4&2209\\4&16\\\hline 87&
609 \\7&609\\\hline &~~0 \end{array}$
Q8 | Ex-3B | Square and Square Roots | Class 8 | Schand Composite Mathematics | myhelper
Question 8
There are 800 children in a school. For a PT drill they have to stand in
a square formation, such that the number of rows is equal to number of
columns. Find the greatest number of children needed to complete the
formation.
Sol :
Total number of student is 800
Given : Number of rows = Number of column=x
Required student t form a square=Number of rows ×Number of column
$=x^{2}=\sqrt{800}$
$\begin{array}{r|l} &28 \\\hline 2&800\\2&4\\\hline 48 & 400
\\8&384\\\hline &~~16 \end{array}$
We can see that square of 28 is less than 800 by 16
∴Required student=800-16=784
MCQS
Q9 | Ex-3B | Square and Square Roots | Class 8 | Schand Composite Mathematics | myhelper
Question 9
Find the correct one:
The square root of 1585081 is
(a) 1259
(b) 2159
(c) 1251
(d) 1291
Q10 | Ex-3B | Square and Square Roots | Class 8 | Schand Composite Mathematics | myhelper
Question 10
Find the value of
\( \sqrt{240.25}+\sqrt{2.4025}+\sqrt{0.024025}+\sqrt{0.00024025}
\)
(a) 1602205
(b) 16.2402
(c) 17.2205
(d) 155.2205
