A Square and a Cube Class 8 Long Question Answer

A Square and a Cube Class 8 Long Question Answer

A Square and a Cube Class 8 Long Question Answer

Question 1.

By which least number, should 1008 be multiplied to make it a perfect square. Then, find the square root of the obtained square.

Solution:

1008 = 2 × 2 × 2 × 2 × 3 × 3 × 7

So, required least number is 7.

The product of 1008 × 7 = 7056

and [latex]\sqrt{7056}[/latex] = 2 × 3 × 3 × 7 = 84.

Question 2.

By which least number should 6912 be divided so that the quotient is a perfect cube. Also, find the cube root of the obtained perfect cube.

Solution:

6912 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3 × 3

So, required least number is 2 × 2 = 4.

Quotient = 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3 × 3

= 1728

Its cuberoot = 2 × 2 × 3 = 12