Name: Number Patterns From Triangles to Squares
Uploaded: 2019-07-19
Duration: 5 min 9 s
Description: Have you heard of Triangular Numbers? Let's understand why the numbers 1, 3, 6, 10, 15, etc., are called triangular. Also, learn how to square big numbers li...

Question

Three numbers are in the ratio

3 : 4 : 5

The sum of their cubes is

0.001728

. Find the numbers.

Accepted Answer

Let the first number be $3 x$

Second number be $4 x$

Third number be $5 x$

Given, that sum of cubes of number is $0.001728$

$∴ {(3 x)}^{3} + {(4 x)}^{3} + {(5 x)}^{3} = 0.001728$

$27 x^{3} + 64 x^{3} + 125 x^{3} = \frac{1728}{1000000}$

$\Rightarrow 216 x^{3} = \frac{1728}{1000000}$

Taking cube root on both sides

$\Rightarrow \sqrt[3]{216 x^{3}} = \sqrt[3]{\frac{1728}{1000000}} \Rightarrow \sqrt[3]{2 \times 2 \times 2 \times 3 \times 3 \times 3 \times x^{3}} = \sqrt[3]{\frac{2 \times 2 \times 3 \times 2 \times 2 \times 3 \times 2 \times 2 \times 3}{10 \times 10 \times 10 \times 10 \times 10 \times 10}}$

$\Rightarrow 6 x = \frac{12}{100}$

$\Rightarrow 6 x = 0.12 \Rightarrow x = 0.02$

Now,

$3 x = 3 \times 0.02 = 0.06$

$4 x = 4 \times 0.02 = 0.08$

$5 x = 5 \times 0.02 = 0.1$

Thus, the numbers are $0.06, 0.08$ and $0.1$

Three numbers are in the ratio $3 : 4 : 5$ The sum of their cubes is $0.001728$ . Find the numbers.

Important Questions on Cubes and Cube Roots

Learn and Prepare for any exam you want !

Three numbers are in the ratio 3:4:5 The sum of their cubes is 0.001728. Find the numbers.

Important Questions on Cubes and Cube Roots

Learn and Prepare for any exam you want !

Three numbers are in the ratio $3 : 4 : 5$ The sum of their cubes is $0.001728$ . Find the numbers.