Q.3) What is the smallest number by which 392 may be divided so that the quotient is a perfect cube? Also, find the cube root of this quotient. (4 marks)
Answers
Answer:
The Battle of Talikota (23 January 1565) was a watershed battle fought between the Vijayanagara Empire and an alliance of the Deccan sultanates who united in order to defeat Aliya Rama Raya. The battle took place at Talikoti, today a town in northern Karnataka, about 80 kilometres (50 mi) to the southeast from the city of Bijapur.
Battle of Talikota
Part of Muslim conquest in the Indian subcontinent
Date 23 January 1565
Location
Talikota in present day Karnataka
16°28′24″N 76°18′43″E
Result
Decisive victory of Deccan Sultanates alliance
Sacking of Vijayanagara
Decline of the Vijayanagara Empire
Belligerents
Deccan sultanates
"Alam" Flag of the Nizam Shahi dynasty of the Ahmadnagar Sultanate.png Ahmadnagar Sultanate
Bijapur Sultanate
QutbshahiFlag.PNG Golkonda Sultanate
Berar Sultanate
Bidar Sultanate
Vijayanagara Empire
Commanders and leaders
"Alam" Flag of the Nizam Shahi dynasty of the Ahmadnagar Sultanate.png Hussain Nizam Shah I
Ali Adil Shah I
QutbshahiFlag.PNG Ibrahim Quli Qutb Shah Wali
Ali Barid Shah I
Burhan Imad Shah
Aliya Rama Raya Executed
Venkatadri †
Tirumala Deva Raya
Achutappa Nayak
Strength
80,000 infantry (Beydurs)[1]
30,000 cavalry[1]
several dozen artillery cannons[1]
140,000 infantry,
10,000 cavalry and
over 100 war elephants[1]
Battle of Talikota is located in KarnatakaBattle of Talikota
Location within Karnataka
The defeat of the Vijayanagara Empire at Talikota, followed by the subsequent destruction and looting of their capital, Vijayanagara, le
In that case 392 × 7 = 2 × 2 × 2 × 7 × 7 × 7 = 2744 which is a perfect cube. Hence the smallest natural number by which 392 should be multiplied to make a perfect cube is 7.
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