Exercise 3B
Question 1
Find by prime factorization the square root of the following numbers :
(i) 2916
(ii) 2704
(iii) 7056
(iv) 9025
(v) 9216
Sol :
Question 2
Find the square root of the following fractions :
(i) $\frac{25}{49}$
(ii) $\frac{196}{484}$
(iii) $\frac{1225}{2025}$
(iv) $0.0009$
(v) $0.00000049$
Sol :
Question 3
Simplify :
(i) $\sqrt{\left(5^{2}-4^{2}\right)}$
(ii) $\sqrt{\left(5^{2}+12^{2}\right)}$
(iii) $\left(\frac{1}{2}\right)^{2}+\sqrt{0.25}$
(iv) $\left(-\sqrt{\frac{4}{9}}\right)\left(-\sqrt{\frac{81}{100}}\right)$
Sol :
Question 4
(i) 6724
(ii) 7921
(iii) 8649
(iv) 9801
(v) 15129
Sol :
Question 5
Find the square root of each of the following decimal numbers by long division :
(i) $4556.25$
(ii) $6099.61$
(iii) $7903.21$
(iv) $9273.69$
Sol :
Question 6
(i) $\sqrt{\frac{2809}{4096}}$
(ii) $\sqrt{\frac{1849}{5776}}$
(iii) $\sqrt{1 \frac{869}{1156}}$
Sol :
Question 7
Find the value of $\sqrt{9216}$ and from this value calculate $\sqrt{92.16}+9.216$.
Sol :
Question 8
Find the square roots of 2116 and 1764 and hence find the value of $\frac{\sqrt{0.2116}+\sqrt{0.1764}}{\sqrt{0.2116}-\sqrt{0.1764}}$.
Sol :
Multiple Choice Questions (MCQs)
Question 9
(a) $\frac{1}{10}$
(b) $\frac{3}{10}$
(c) 1
(d) 10
Sol :
Question 10
Of the numbers $0.16, \sqrt{0.16},(0.16)^{2}$ and $0.016$ the least number is
(a) $(0.16)^{2}$
(b) $\sqrt{0.16}$
(c) $0.016$
(d) $0.16$
Sol :
Question 11
$\sqrt{0.0025} \times \sqrt{2.25} \times \sqrt{0.0001}$ equals
(a) $0.000075$
(b) $0.0075$
(c) $0.075$
(d) $0.00075$
Sol :
Question 12
(a) $2 \frac{35}{64}$
(b) $1 \frac{33}{62}$
(c) $1 \frac{17}{62}$
(d) $2 \frac{23}{62}$
Sol :
Question 13
(a) 1
(b) 0.65
(c) 0.45
(d) 0.54
Sol :
Question 14
3600 soldiers are asked to stand in different rows. Every row has as many soldiers as there are rows. Find the number of rows.
Sol :
Question 15
Find the perimeter of a square whose area is $6889 \mathrm{~m}^{2}$.
Sol :
Question 16
A society collected ₹ 8836, each member contributing as many rupees as there were members. Find the number of members of the society.
Sol :
Question 17
In a basket there are 1250 flowers. A man goes for worship and puts as many flowers as there are temples in the city. Thus he needs 8 baskets of flowers. Find the number of temples in the city.
Sol :
Question 18
What should be subtracted from 6249 to get a perfect square number? What is this perfect square number? Also, find its square root.
Sol :
Question 19
What least number must be added to 594 to make the sum a perfect square ?
Sol :
Question 20
What would be added to 7912 to make the sum a perfect square ?
Sol :
Question 21
Find the least number of six digits which is a perfect square.
Sol :
Question 22
A General arranges his soldiers in rows to form a perfect square. He finds that in doing so, 60 soldiers are left out. If the total number of soldiers be 8341 , find the number of soldiers in each row.
Sol :
High Order Thinking Skills (HOTS)
Question 23
Find $: \sqrt{10+\sqrt{25+\sqrt{108+\sqrt{154+\sqrt{225}}}}}$
Sol :
Question 24
Find the value of $\sqrt{1191.16+70 \sqrt{129.96}}$.
Sol :
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