What is the square root of 3025?

Question

You are told 3025 is a perfect square whose root ends in 5. What is \sqrt{3025}? Aim: under 6 seconds.

Accepted Answer

The forward trick says a number ending in 5 squares to 100\,n(n+1) + 25: the last two digits are always 25, and the leading part is n(n+1). Reverse it. Strip the trailing 25 from 3025 to leave 30, then find n with n(n+1) = 30 \quad\Rightarrow\quad n = 5 \ (	ext{since } 5 	imes 6 = 30). So the root is 10n + 5 = 55, and indeed 55^2 = 3025. The check that a number can come from this trick: it must end in 25, and the number formed by the remaining digits must be a product of two consecutive integers. For 5625 	o 56 = 7 	imes 8 \Rightarrow \sqrt{5625} = 75. For 9025 	o 90 = 9 	imes 10 \Right…

What is the square root of 3025?

Your answer

More Mental Math questions