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# square of the integer is a two-digit integer?

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How many different integers are there such that the square of the square of the integer is a two-digit integer?

mathtoo  Dec 29, 2017
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#1
+91451
+2

Write down a list of squared numbers and count them

1^2=1                  1^2=1

2^2=2*2=4          4^2=16

3^2=3*3=9           9^2=81

etc

For every positive number there will be a negative one as well, so you better double your answer :)

Melody  Dec 29, 2017
edited by Melody  Dec 29, 2017
edited by Melody  Dec 29, 2017
#6
+91451
+2

The square of the square is a power of 4

1^4 id 1 digit

2^4=16 which is 2 digit

3^4=81 so that works

4^4=256 which is too big

so I get

2, 3, -2, and -3  that is it.

4 integers meet this requirment :)

Melody  Dec 29, 2017
#2
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tertre  Dec 29, 2017
#3
+5931
+1

*edit*

This answer was wrong...I agree with Melody.

hectictar  Dec 29, 2017
edited by hectictar  Dec 29, 2017
#4
+1364
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hmm, not getting the same answer..

tertre  Dec 29, 2017
#5
+5931
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