CBSE Class 8 - Maths - CH 6 - Square and Square Roots (Ex 6.4)

Square and Square roots

Exercise 6.4

Q1: Find the square root of each of the following numbers by 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

Answer:

(i)The square root of 2304 is calculated as follows.

	48
4	23 04 -16
88	704 704
	0

∴√ 2304  = 48

(ii)The square root of 4489 is calculated as follows.

	67
6	44 89 -36
127	889 889
	0

∴√ 4489  = 67

(iii)The square root of 3481 is calculated as follows.

	59
5	34 81 -25
109	981 981
	0

∴√ 3481  = 59

(iv)The square root of 529 is calculated as follows.

	23
5	5 29 -4
43	129 129
	0

∴√ 529  = 23

(v)The square root of 3249 is calculated as follows.

	57
5	32 49 -25
107	749 749
	0

∴√ 3249  = 57

(vi)The square root of 1369 is calculated as follows.

	37
3	13 69 -9
67	469 469
	0

∴√ 1369  = 37

(vii)The square root of 5776 is calculated as follows.

	76
7	57 76 -49
146	876 876
	0

∴√ 5776  = 76

CBSE Class 8 - Maths - Cube and Cube Roots (Ex 7.1)

Cube and Cube Roots 

(NCERT Ex 7.1)

Q1: Which of the following numbers are not perfect cubes?
(i)  216
(ii) 128
(iii) 1000
(iv) 100
(v) 46656

Answer:

(i) The prime factorisation of 216 is as follows:

2	216
2	108
2	54
3	27
3	9
3	3
	1

∴ 216 = 2 ☓ 2 ☓ 2 ☓ 3 ☓ 3 ☓ 3 = 2³ ☓ 3³

Here, each prime factor appears as many times as a perfect multiple of 3, therefore, 216 is a
perfect cube.

(ii) The prime factorisation of 128 is as follows:

2	128
2	64
2	32
2	16
2	8
2	4
2	2
	1

∴  128 = 2 ☓ 2 ☓ 2 ☓ 2 ☓ 2 ☓ 2 ☓ 2

Here, each prime factor does not appear as many times as a perfect multiple of 3. Therefore, 128 is not a perfect cube.

(iii)The prime factorisation of 1000 is as follows.

2	1000
2	500
2	250
5	125
5	25
5	5
	1

∴ 1000 = 2 ☓ 2 ☓ 2 ☓ 5 ☓ 5 ☓ 5 =  2³ ☓ 5³

Here, as each prime factor appears as many times as a perfect multiple of 3, therefore, 1000 is a perfect cube.

(iv)The prime factorisation of 100 is as follows.

2	100
2	50
5	25
5	5
	1

∴ 100 = 2 ☓ 2 ☓ 5 ☓ 5

Here, each prime factor does not form triplet group(s). Therefore, 100 is not a perfect cube.

(iv) The prime factorisation of 46656 is as follows.

2	46656
2	23328
2	11664
2	5832
2	2916
2	1458
3	729
3	243
3	81
3	27
3	9
3	3
	1

46656 = 2 ☓ 2 ☓ 2 ☓ 2 ☓ 2 ☓ 2 ☓ 3 ☓ 3 ☓ 3 ☓ 3 ☓ 3 ☓ 3
 = 2³ ☓ 2³ ☓ 3³ ☓ 3³
Here, each prime factor appears as many times as a perfect multiple of 3,
∴ 46656 is a perfect cube.

Q2: Find the smallest number by which each of the following numbers must be multiplied to obtain a perfect cube.

CBSE Class 6 - History - CH 11 - New Empires and Kingdoms

New Empires and Kingdoms

Coin showing Samudraguta with Garuda pillar
credits:wikimedia

(Q & A)

Q1: Name the famous rulers of Gupta dynasty?

Answer: Samudragupta and Chandragupta II (Vikramaditya)


Q2: What do you mean by Prashasti?

Answer:  Prashasti, a Sanskrit word, meaning ‘in praise of’. Generally, it is an inscription written in praise of  rulers. It also tells about the genealogy of the rulers.


Q3: Who composed Prashasti of Samudragupta and where it is inscribed at?

Answer: Harishena composed a long poem in praise of King Samudragupta. It is inscribed on Ashokan pillar at Allahabad.


Q4: What was the old name of Allahabad?

Answer: Prayag


Q5: Who was the founder of Gupta dynasty?

Answer: Chandragupta I


Q6: Write a short note on Chandragupta I

Answer:

1. Chandragupta I, the first ruler of Gupta dynasty, ascended throne of Magadha in 320 AD.
2. He married to Kumaradevi, a princess of Lichchavi tribe.
3. He expanded his kingdom upto Allahabad and took the title of Maharajadhiraj.

CBSE Class 7 - Science - CH 14 - Electric Current and Its Effects (MCQs)

Electric Current and its Effects
(MCQs)

Why CFL is better than electric bulb?

Q1: The unit to measure electric resistance is:
 
(a) Joule
(b) Ohm
(c) Ampere
(d) Volt


Q2: The device used to make or break an electric circuit is:

(a) Resistor
(b) Battery
(c) Switch
(d) Ammeter


 
Q3: When an electric current passes through a solenoid, it acts as a/an

(a) insulator
(b) electric bell
(c) resistor
(d) bar magnet


Q4:  Which of the following is an essential element in an electric circuit?

CBSE Class 8 - Maths - Comparing Quantities (Ex 8.2)

Comparing Quantities 

NCERT Chapter (Ex 8.2)

Q1:A man got a 10% increase in his salary.If his new salary is 1,54,000,find his original salary.
Answer:

Let original salary be x. Given that new salary is 1,54,000.

Original salary + increment= New salary

But it is given that increment is 10% of the original salary.

Therefore,







Thus,the original salary was Rs 1,40,000.

Q2: On Sunday 845 people went to the zoo.On Monday only 169 people went.What is the percent decrease in the people visiting zoo on Monday?

Answer:

Given that on Sunday,845 people went to the zoo and on Monday,169 people went.

Decrease in number of people = 845-169=676

Percentage Decrease

CBSE Class 9 - Science - CH6 - Natural Resources (MCQs)

Natural Resources

(MCQs)

Ozone Layer
credits:classroomclipart

Q1: Corbett National Park is famous for?

(a) Neel Gai
(b) Snakes
(c) Rhinoceros
(d) Tigers


Q2: Green plants of an ecosystem are called.

(a) Producers
(b) Decomposers
(c) Consumers
(d) None of these


Q3: Energy flow in the ecosystem is

(a) unidirectional
(b) bidirectional
(c) multidirectional
(d) none of these


Q4: Two important groups of detritivores are

(a) Animals and Plants
(b) Prokaryotes and Algae
(c) Prokaryotes and Fungi
(d) Plantae and Prokaryotes

CBSE Class 10 - English Communcation - Letters

Letters

Q(CBSE 2012): Look at the following poster denouncing dowry. Based on the picture and using your own ideas write a letter, in about 120 words, to the editor of a national daily expressing your views on the evils of dowry and how this problem needs to be tackled.

Answer:

X-Lane
Y-city
19th December,2013
The Editor
The Hindustan Times
New Delhi

Dear Editor

Through the coloumns of your esteemed newspaper, I would like to draw the attention of the people towards the burning issue of dowry and its ill-effects on our society.

The dowry system is a social evil. In India many of the traditional customs have been given up, but the custom of dowry has not only continued, but flourished over the years.In spite of increase in the literacy rate, education and modernization, we have not been able to eradicate this problem from our society. Even today, daughters are given furniture, crockery, electronic items, jewellery, cars, flats etc. in order to ensure their security. Initially dowry was given to support the new couple, but with the passage of time marriage has become an occasion for blatant selling of the bridegroom. The ill-effects of this problem include the neglect of daughters, sex-selective abortion, female infanticide, and the harassment, abuse etc. When demands for dowry are not met, the bride is subjected to torture, and often even killed.