Olympiad Test: Cube And Cube Roots - Class 8 MCQ

343 = 7 × 7 × 7
∴ 343 is a perfect cube.

500 = 2 × 5 × 5 × 5 = 2 × 5³

∴ 12 should be added to make the sum, a perfect cube

To find the least number that should be subtracted from 1370 to make the resultant a perfect square, we first calculate the square root of 1370, which is approximately 37.05. The perfect squares closest to 1370 are 37²=1369 and 38²=1444. The nearest perfect square smaller than 1370 is 1369. Subtracting 1369 from 1370 gives: 1370−1369=1

Thus, the least number that should be subtracted from 1370 to make the result a perfect square is 1.

= 0.004

 will have (19 – 9) has one of its factors
∴ 10 will be a factor of (193 – 93)

21³ + 27³ has (21 + 27) as its one of the factors
∴ 48 will be a factor of (21³ + 27³)

1720 > 1000 = 10³ 
∴ 11³ = 1331, 12³ = 1728
∴ 1728 – 1720 = 8 should be added to 1720 to make the sum, a perfect cube.