Exercise 3B
Question 1
Find the two square roots of the following numbers.
(a) 4
Sol : 2,-2
(b) 81
Sol : 9,-9
(c) 196
Sol : 14,-14
(d) 400
Sol : 20,-20
(e) 441
Sol : 21,-21
(f) 0.0049
Sol : 0.07, -0.07
(g) 0.0001
Sol : 0.01, -0.01
(h) $3\frac{1}{16}$
Sol : $\frac{7}{4},-\frac{7}{4}$
(i) $2\frac{1}{4}$
Sol : $\frac{3}{2},-\frac{3}{2}$
(j) 0.0289
Sol : 0.17 , -0.17
Question 2
Evaluate the following.
(a) √36
Sol :
=2×2×3×3
=2×3
=6
(b) -√9
Sol : =-(3×3)
=-3
(c) √121
Sol : =11×11×11
(d) -√225
Sol :
=-(5×5×3×3)
=-(5×3)
=-15
(e) √361
Sol :
=19×19
=19
(f) √900
Sol :
=30×30
=30
(g) √0.09
Sol :
=0.3×0.3=0.3
(h) √0.0256
Sol :
=0.16×0.16
=0.16
(i) √2.25
Sol :
=1.5×1.5
=1.5
(j) $\sqrt{4\frac{25}{36}}$
Sol :
$=\frac{13}{6}$
Question 3
Solve
(a) x2 = 1
Sol : x=±1
(b) 12x2 = 108
Sol :
$x^2=\frac{108}{2}=9$
x=±3
(c) x2 – 17 = -1
Sol :
x2=-(16)
x=±4
(d) x2=$\frac{16}{25}$
Sol :
x2=$\pm \frac{4}{5}$
Question 4
Find the square root of each of the following numbers by the prime factorisation method.
(a) 484
Sol :
=2×2×11×11
=2×11=22
(b) 2500
Sol :
=2×2×5×5×5×5
=2×5×5
=50
(c) 2025
Sol :
=5×5×9×9
=5×9
=45
(d) 2916
Sol :
=2×2×3×3×9×9
=2×3×9=54
(e) 2401
Sol :
=7×7×7×7
=7×7=49
(f) 6084
Sol :
=2×2×3×3×13×13
=2×3×13=78
(g) $1\frac{184}{441}$
Sol :
$=\frac{625}{441}=\frac{25\times 25}{21\times 21}$
$=\frac{25}{21}$
(h) 0.1936
Sol :
$=\frac{1936}{10000}=\frac{44\times 44}{10\times 10\times 10 \times 10}$
$=\frac{44}{100}$=0.44
(i) 0.0576
Sol :
$=\frac{576}{10000}=\frac{24\times 24}{10\times 10\times 10\times 10}$
$=\frac{24}{100}$=0.24
(j) 40.96
Sol :
$=\frac{4096}{100}=\frac{2\times 2\times 2\times 2\times 2\times 2\times 2\times 2\times 2\times 2\times 2\times 2\times }{10\times 10}$
$=\frac{64}{100}$=0.64
Question 5
Find the smallest whole number for each of the following numbers by which it should be multiplied so as to get a perfect square number.
(a) 768
Sol :
=2×2×2×2×2×2×2×2×3
∴Multiplied by 3
(b) 200
Sol :
=5×5×2×2×2
∴Multiplied by 2
(c) 2880
Sol :
=2×2×2×2×2×2×3×3×5
∴Multiplied by 5
(d) 16807
Sol :
=7×7×7×7×7
∴Multiplied by 7
(e) 1331
Sol :
=11×11×11
∴Multiplied by 11
Question 6
Find the smallest whole number for each of the following numbers by which it should be divided so as to get a perfect square number.
(a) 3125
Sol :
=5×5×5×5×5
∴Divided by 5
(b) 1800
Sol :
=2×2×2×5×5×3×3
∴Divided by 2
(c) 1008
Sol :
=2×2×2×2×3×3×7
∴Divided by 7
(d) 6912
Sol :
=2×2×2×2×2×2×2×2×3×3×3
∴Divided by 3
(e) 2925
Sol :
=13×15×15
∴Divided by 13
Question 7
Find the smallest square number that is divisible by each of the numbers 8, 15 and 20.
Sol :
⇒8,15 & 20
⇒L.C.M of 8,15,20 is 120
∴Prime factor of 120=2×2×[2×3×5]
=30
∴The factor 30 remains unpaired so to make 120 a perfect square it should be multiplied by 30
∴The smallest square number=120×30
=3600
Question 8
Find the least square number, which is exactly divisible by 3, 4, 5, 6 and 8.
Sol :
L.C.M of 3,4,5,6,8=120
∴Prime factor of 120=2×2×[2×3×5]
=30
∴Least square number=120×30
=3600
Question 9
The area of a square plot is $101 \frac{1}{400}$ meter square, Find the length of one side of the plot.
Sol :
ATQ
$a^2=101\frac{1}{400}$ m2
∴$a=\sqrt{101\frac{1}{400}}=\sqrt{\frac{40401}{400}}$
∴$a=\pm \frac{201}{20}=10\frac{1}{20}$
∴One side of plot$=10\frac{1}{20}$ m
Question 10
Find the value of $=\sqrt{162+\sqrt{38 + \sqrt{121}}}$
Sol :
$=\sqrt{162+\sqrt{38+11}}$
$=\sqrt{162+\sqrt{49}}=\sqrt{162+7}$
=√169=13
Question 11
Given that √3136 = 56, find the value of √31.36 + √0.3136
Sol :
=√31.36 + √0.3136
$=\sqrt{\frac{3136}{100}}+\sqrt{\frac{3136}{10000}}$
$=\frac{56}{10}+\frac{56}{10}$
$=\frac{560+560}{1000}$
$=\frac{616}{100}$=6.16
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