Write
(i) 10² and
(ii) 112 as the sum of consecutive odd natural numbers

Examine if each of the following is a perfect square:
(i) 725
(ii) 190
(iii) 841
(iv) 1089

Find the least square number which is divisible by each of the numbers 8,12 and 15.

Find the square root by long division method.
(i)17956
(ii) 11025
(iii) 6889
(iv) 1764
(v) 418609

Find the square root of each of the following fractions.
(i) \(\cfrac { 144 }{ 221 } \) 
(ii) \(7\cfrac { 18 }{ 49 } \) 
(iii) \(6\cfrac { 1 }{ 4 } \) 
(iv) \(4\cfrac { 25 }{ 36 } \)

Find two smallest perfect square numbers which when multiplied together gives a perfect cube number

What is the square root of cube root of 46656?

Find the smallest number by which 200 should be multiplied to make it a perfect cube.

Evaluate:\(\left( \cfrac { 1 }{ 2 } \right) ^{ -5 }\)

Evaluate:\(\left( { 2 }^{ -5 }\div { 2 }^{ 7 } \right) \times { 2 }^{ -2 }\)

Evaluate:(5⁰ + 6^{- 1}) x 3³

Evaluate : (3^-1 + 4^-2 + 5^-3)⁰

Simplify:\(\cfrac { { 9 }^{ 2 }\times { 7 }^{ 2 }\times { 2 }^{ 5 } }{ { 84 }^{ 3 } } \)

Evaluate:
\(\cfrac { { 10 }^{ x } }{ { 10 }^{ -3 } } ={ 1 }0^{ 9 }\)

A square carpet covers an area of 1024 m² of a big hall. It is placed in the middle of the hall. What is the length of a side of the carpet?

2401 plants are planted in a garden such that each contains as many plants as the number of rows. Find the number of rows and the number of plants in each row.

If (625)^x 15625, x = find x² and x³.

A greeting card has an area 90 cm². Between what two whole numbers is the length of its side?

A group of 1536 cadets wanted to have a parade forming a square design. Is it possible? If it is not possible how many more cadets would be required?

Evaluate:\(\sqrt { 286225 } \) and use it to compute \(\sqrt { 2862.5 } +\sqrt { 28.6225 } \)

Simplify: (3.769 x 10⁵) + (4.21 x 10⁵)

210 men working 12 hours a day can finish a job in 18 days. How many men are required to finish the job in 20 days working 14 hours a day?

A soap factory produces 9600 soaps in 6 days working 15 hours a day. In how many days will it produce 14400 soaps working 3 hours more a day?

A can do a piece of work in 12 hours, B and C can do it 3 hours whereas A and C can do it in 6 hours. How long will B alone take to do the same work?

Carpenter A takes 15 minutes to fit the parts of a chair while Carpenter B takes 3 minutes more than A to do the same work. Working together, how long will it take for them to fit the parts for 22 chairs?