Question

Sum of certain number and its positive square root is 90 the number is

Answer 1

Let the positive square root be 'x'
The number is x^2

x^2 +x = 90

x^2+x-90=0
x^2 +10x-9x-90= 0
x(x+10)-9(x+10) =0

X=9, x=-10
x cannot be -10 because square root is positive number.

there x = 9

The number is 81.

Hope this helps.

Answer 2

The number is 81

Given :

Sum of certain number and its positive square root is 90

To find :

The number

Solution :

Step 1 of 2 :

Form the equation to find the number

Let the required number = x²

Then positive square root of the number = x

By the given condition

x² + x = 90

Step 2 of 2 :

Find the number

x² + x = 90

⇒ x² + x - 90 = 0

⇒ x² + (10 - 9)x - 90 = 0

⇒ x² + 10x - 9x - 90 = 0

⇒ x(x + 10) - 9(x + 10) = 0

⇒ (x + 10)(x - 9) = 0

Now ,

x + 10 gives x = - 10

x - 9 = 0 gives x = 9

Since we are concerned about positive square root

∴ x ≠ - 10

∴ x = 9

Hence the required number

= x²

= 9²

= 81

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