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# Math help pleas

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Intern
Joined: 16 May 2016
Posts: 1

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16 May 2016, 16:19
If a natural number is entered into a new toy names Squareroo, the toy will do the following:
(1) Find the perfect square closest to the number entered;
(2) Take the square root of the perfect square;
(3) Find the perfect square closest to the square root in step 2;
(4) Repeat the steps of taking the square root and finding closest perfect square until it takes the square root of the same number twice.

How many times does Squareroo take the square root if the number entered into it is 660?

I tried this problem and I got 5, but I don't know if I'm right or if my work is right, so any answers will be greatly appreciated. Thanks so mych
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 6227
GMAT 1: 760 Q51 V42
GPA: 3.82

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14 Mar 2017, 16:02
IndianSavage wrote:
If a natural number is entered into a new toy names Squareroo, the toy will do the following:
(1) Find the perfect square closest to the number entered;
(2) Take the square root of the perfect square;
(3) Find the perfect square closest to the square root in step 2;
(4) Repeat the steps of taking the square root and finding closest perfect square until it takes the square root of the same number twice.

How many times does Squareroo take the square root if the number entered into it is 660?

I tried this problem and I got 5, but I don't know if I'm right or if my work is right, so any answers will be greatly appreciated. Thanks so mych

(1) $$676 = 26^2$$ is the perfect square closest to $$660$$.
(2) The square root of the perfect square $$676$$ is $$26$$.
(3) $$25 = 5^2$$is the perfect square closest to $$26$$.
(4) The square root of the perfect square $$25$$ is $$5$$.
(5) $$4 = 2^2$$ is the perfect square closest to $$5$$.
(6) The square root of the perfect square $$4$$ is $$2$$.
(7) $$1 = 1^2$$ is the perfect square closest to $$2$$.
(8) The square root of the perfect square $$1$$ is $$1$$.

Squareroo took the square root from the above $$4$$ time at step (2), (4), (6) and (8).

My answer is $$4$$.
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Re: Math help pleas &nbs [#permalink] 14 Mar 2017, 16:02
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# Math help pleas

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