Exercise 3 (B)
Q1 | Ex-3B | Square and Square Roots | Class 8 | Schand Composite Mathematics | myhelper
Question 1
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 :
(iv) 75625
Sol :
(v) 166464
Sol :
(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×side13689=side2
$\begin{array}{r|l} &117 \\\hline 1&13689\\1&1\\\hline 21& ~~36 \\1&~~21\\\hline 227&~~1589\\7&~~1589\\\hline& ~~~~0 \end{array}$
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
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
There are no solutions here please fix this
ReplyDeleteWhy solutions are not getting here
ReplyDeleteHere is not givien solution
ReplyDeleteSolution is not given
ReplyDeleteFor those who cannot find the solution here:
ReplyDeleteThe answer of no.9 is 1259
And the answer of no.10 is 17.2205