Explanation for Question 4 From the Math (Calc) Section on the Official Sat Practice Test 9
Question four, it gives us the expression. 2 The square root of X squared is equal to X. 3 And it says, which of the following values of X is not a solution 4 to the equation above. So in order to solve 5 this one, let's really think about what it's asking. 6 A lot of, you might look at this and say, okay, well, this is 7 true for every, every X given the fact that we've 8 written X squared to the one half, and hopefully you're familiar with exponent rules 9 and you understand that you're going to multiply these things by each other. 10 And you think that it might just be X to the first power. 11 The problem with that is, is this that the square root of X 12 squared or just the square root of X has a domain limitation, 13 or excuse me, it has a, um, a range limitation. 14 So if you think about what the graph of the squared of X looks 15 like, it looks like this. 16 There aren't any negative values in it. And this will make more sense. 17 Once we plug in the only native value that we're given, 18 which in fact is not a solution to the equation above. 19 So we have negative four squared. 20 The square root should be equal to negative four, 21 but negative four squared is equal to 16 because a negative 22 number of times itself, or a negative number times a negative number in other 23 words is equal to a positive number. So now we have the squared of 24 16 is equal to negative four, and we know that that's not true. 25 Four does not equal negative four. So that's why we pick answer choice.