Question

The product of two consecutive square numbers is 144. Work out the two numbers

Answer 1

9 and 16

Explanation:

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Answer 2

Let the first number be = x

Let the second number which is consecutive be = x+1

As given, the product of two consecutive square numbers is 144

`x^(2)*(x+1)^(2)=144`

Square rooting both sides we get

`x(x+1)=12`

`x^(2)+x=12`

`x^(2)+x-12=0`

`x(x+4)-3(x+4)=0`

`(x-3)(x+4)=0`

`x=3` or
`x=-4`

Neglect the negative value so we get x=3

Hence, one number is 3 and the consecutive number is = 3+1=4

The square of the numbers are 9 and 16.