Express
(i) 15² and
(ii) 19² as the sum of two consecutive positive integers.

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

Find a Pythagorean triplet whose
(i) largest member is 65
(ii) smallest member is 10

Find the square root of the following by repeated subtraction method.
(i) 144
(ii) 256
(iii) 784

Find the smallest number by which 10985 should be divided so that the quotient is a perfect cube.

Find the cube root of 729 and 6859 by prime factorisation

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

Evaluate:\(\left( -\cfrac { 1 }{ 3 } \right) ^{ -2 }\)

Evaluate:(5⁰ + 6^{- 1}) x 3³

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