Question

three numbers are in ratio 2:3:4.if the cube root of the smaller number is 5 then find the cube root of larger number

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Answer 1

Answer:

Three numbers are in the ratio 2 : 3 : 4 (given)

so let the numbers be 2x, 3x and 4x respectively

sum of their cubes is 792

It can be written as,

( 2x )^3 + ( 3x )^3 + ( 4x )^3 = 792

8x^3 + 27x^3 + 64x^3 =792

x^3 is the common term so it can be taken out,

x^3 ( 8 + 27 + 64 ) =792

99 x^3 = 792

x^3 = 792 / 99

x^3 = 8

x = cube root of 8

x = 2

2x = 2*2 = 4

3x = 3*2 = 6

4x = 4*2 = 8

so the numbers are 4, 6 and 8

average of the three numbers = 4 + 6 + 8 / 3

average = 18 / 3 = 6

Hence the average of the numbers is 6.

checking the values,

The ratio of these numbers 4 : 6 : 8 is 2 : 3 : 4

Also,

cube of first number, 4 = 64

cube of second number, 6 = 216

cube of third number, 8 = 512

sum of the cubes = 64 + 216 + 512 = 792

Hence verified.

Step-by-step explanation:

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