Model 3 Simplification based on cube & cube root Practice Questions Answers Test with Solutions & More Shortcuts

Answer: (b)

Expression = $(√{4^3 + {15}^2})^3$

= $(√{64 + 225})^3 = (√289)^3$

= $(17)^3$ = 4913

Answer: (a)

$(5.5)^3 - (4.5)^3$

= $(5.5 - 4.5)^3$ + 3 × 5.5 × 4.5 (5.5 - 4.5)

= $(1)^3$ + 74.25(1)

= 1 + 74.25 = 75.25

Answer: (d)

Expression = $√^3{4{12}/125}$

= $√^3{512/125} = √^3{{8 × 8 × 8}/{5 × 5 × 5}} = 8/5$ =1.6

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

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.