Q15 of 67 Page 168

Find two smallest perfect squares whose product is a perfect cube.


Hence, 4 and 16 are the two smallest perfect squares whose product is a perfect cube.


More from this chapter

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12

Can 1010 be written as a difference of two perfect squares? [Hint: How many times 2 occurs as a factor of 1010?]

 13

What are the remainders when a perfect cube is divided by 7?

 14

What is the least perfect square which leaves the remainder 1 when divided by 7 as well as by 11?

 16

Find a proper positive factor of 48 and a proper positive multiple of 48 which add up to a perfect square. Can you prove that there are infinitely many such pairs?