Model 3 Simplification based on cube & cube root Section-Wise Topic Notes With Detailed Explanation And Example Questions

Answer: (c)

First number = $(√5)^2 = 5$

Let the second number be x.

$x^2 + 5^2 = 146$

$x^2$ = 146 –25 = 121

$x = √{121} = 11$

Cube of 11 =1331

Answer: (d)

4320 = 2 × 2 × 2 × 2 × 2 × 3 × 3 × 3 × 5

= $2^3 × 3^3 × 2^2 × 5$

Required number = 2 × 5 × 5 = 50

Answer: (a)

343 = 7 × 7 × 7

125 = 5 × 5 × 5

81 = 3 × 3 × 3 × 3

64 = 8 × 8 = 4 × 4 × 4

We see that 343 and 125 are only perfect cubes of 7 and 5 respectively.

81 is only a perfect square of 9. 64 is a perfect square of 8 as well as a perfect cube of 4.

Answer: (d)

On simplification,

Expression = $2/4 × 7/10 × 5$

= $7/4 = 1{3}/4$

Answer: (d)

1944 = 2×2×2×3×3×3×3×3 = $2^3 × 3^3 × 3^2$

Clearly, 1944 should be multiplied by 3 to make the result a perfect cube.

Answer: (c)

We know that

$a^3 + b^3 + c^3$ - 3abc

= (a+b+c)$(a^2+b^2+c^2$ - ab - bc - ca)

= $1/2 (a + b + c) [(a - b)^2 + (b - c)^2 + (c - a)^2 ]$

∴ $√^3{(333)^3 + (333)^3 + (334)^3 - 3 × 333 × 333 × 334}$

= $√^3{1/2 (333 + 333 + 334)[(333 - 333)^2 + (333 - 334)^2 + (334 - 333)^2]}$

= $√^3{1/2 × 1000 × 2} = √^3{1000}$

= $√^3{10 × 10 × 10}$ = 10