It is 8th grade homework that student nor parents can solve. It is a square root problem. The work has to be shown.

Grigori:

**The difference between the square roots of a number is 30. What is the number?**

Analytical approach.

Let the required number be denoted by x

^{2}. The square root of x

^{2}is (+ or -) x. If you take the second number as + x (that is x itself) the difference is x - x = 0, not 30. So that you must choose the second number as - x. The difference between + x and - x is equal to x - (-x) = 2x. We are given that this difference is 30. Therefore, 2x = 30. That is x = 15, and the required number is 15

^{2}= 225.

Back check: Square roots of 225 are +15 and -15. Their difference is 15 – (15) = 30. Hurray!

Dattaprabhakar (Dr. G.)

P.S. Generalization (for adavnced students): If M is any real number, the number (M/2)

^{2}is such that the difference between its square roots is M. Proof: On request. Post a comment if you rrrrrreeeeeallllllyyyyy want to see it.