<p>Each of the following integers has some of its digits covered, which of these integers could be the square of an integer?
A)<strong><em>,328
B)</em></strong>,342
C)<strong><em>,447
D)</em></strong>,598
E)___,729
Plz answer me and explain it with every detail...
and THANX</p>
<p>A)<strong><em>,328
B)</em></strong>,342
C)<strong><em>,447
D)</em></strong>,598
E)___,729</p>
<p>Consider the units digit of a number (N) whose square must equal one of the above. The square of the units digit of N can be: (0^2, 1^2, etc.)</p>
<p>0,1,4,9,16,25,36,49,64,81</p>
<p>This eliminates choices A), B), C), D) . That leaves E)</p>
<p>The number must be …7. The “…” are to-be-done. The question doesn’t require that we determine them.</p>
<p>If this approach is unclear think about what you do when you multiply two numbers. What is the step that leads to the units digit of the product? Try 77x77= (70+7)x(70+7)=70x70 + 2x7x70 +7x7. Note that the units digit of the first two terms is 0. Only the units digit matters.</p>
<p>i understood the first way and the second , but the first way doesn’t always works .
For example: 26^2=676 , which contains units digit “6” - that is not a square of an integer.
and thanxx</p>
<p>But the ending unit digit 6 is not one of the choices. The point is not that the result of the multiplication is a square of an integer, but that the units digit of the result is predictable. The statement of the question masks the simplicity of the solution.</p>
<p>The “second” method is simply an explanation of the first. I picked a 2 digit-number to show that. When you multiply two multi-digit integers the units digit of the result depends only on the units digit of the respective numbers. Just do a simple multiplication problem to see this:</p>
<p>…273
…143
…----
…819
…1092
…273
…--------
…39039</p>
<p>The 9 could have been predicted 3x3 – (respective units digit of 273 and 143).</p>
<p>The recipe above is really the same as (270 + 3)x(140 + 3) etc.</p>
<p>The question is testing your basic understanding of multiplication. It’s really much simpler than it looks.</p>
<p>If you’re really confused and this was an actual question on the test, can’t you just put this in your calculator and see the square root of each number?</p>
<p>^Yes you can</p>
<p>I had this exact question on the sunday SAT for March. Where’d you get this question from, OP?</p>
<p>@Kevycanuck No, you can’t because you don’t know the first X digits (looks like a 6 digit number with the first 3 covered but it’s not explicit).</p>
<p>@cortana</p>
<p>Dude, this exact question was on my SAT and the proctor, who’s also a math teacher, told me ___, 729 is correct because its the only number who has an integer square root (27). (He told me a week after the test, of course)</p>
<p>And yes, it’s XXX,729</p>
<p>I’m willing to be $$$$$$$ on this.</p>
<p>(of course, I might just be overlooking the question and might be missing somehting. but I’m almost positive)</p>
<p>That is the right answer, but for the reason fogcity gave. The last three digits do not need to be a perfect square. For instance 388,129 = 623^2, but 129 is not a perfect square.</p>