A Squared Year

Number Theory Level 2

What is the smallest perfect square whose first four digits is 2015?

Note: Give the value of the perfect square.

The answer is 20151121.

1 solution

Rajen Kapur
Apr 14, 2016

As $\sqrt{2015}=44.88875137$ and $449^2=201601$ fails as also $\sqrt{20150}=141.9506957$ fails to either have $141^2$ or $142^2$ correct choices and then $4489^2= 20151121$ is the answer.

Can you explain in more detail? Why do we look at $\sqrt{2015}$ ?

Note: Your solution is actually incomplete. See this problem .

Calvin Lin Staff - 5 years, 2 months ago

I have edited the solution by correcting the missed step. Thanks.

Rajen Kapur - 5 years, 2 months ago

That's better. Your approach suggests that we have to test a bunch of values till we find the actual answer.

What are the relevant inequalities to look at to figure out what the answer should be? E.g. What if we wanted a square that started with 123456789?

Calvin Lin Staff - 5 years, 2 months ago

A Squared Year

The answer is 20151121.

1 solution

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