Rewrite each expression without the absolute value bars. |√2-1|

Question

Accepted Answer

Welcome back. I'm so glad you're here. We're evaluating this expression to remove the absolute value bars. And what makes it a little bit different is that it's got that square root inside of the absolute value bars. So we're going to remove those but we're going to think of the number as a decimal around a decimal in order to think about what we're doing on the right hand side as we remove those absolute value bars from the square root one. So I'll copy that down on the right. We've got negative absolute value of the squared of -5. And thinking about the squared of three. Okay, one squared is 12 squared is four. So something between one and two, two squared will give us three. We can use a calculator and that tells us that approximately 1.73 squared will get us three. So we've got 1.73 minus five. On the decimal side these two are equivalent and now we can do that 1.73 minus five, That is negative. 3.27. And so that means on the right hand side, the square root of 3 -5 is a negative value inside those absolute value bars and that makes sense. A small number minus a bigger number is going to be a negative. And so when we want to get rid of the absolute value bars, what we're really asking is how far away is this value from zero? The number inside is negative but it is a value from zero. That's going to be a positive number negative 3.27 is 3.27 units away from zero. So that gets rid of our absolute value bars on the right hand side we know that that's a negative number on the number line but it's a positive amount away from zero. And that positive amount is about 3.27 units. And how do we express 3.27 units? Well that would be the same as if we took the bigger number five minus the smaller number the square root of three. That is approximately 3.27. So that gets rid of our absolute value lines and now we carry down that negative and all we have to do is distribute the negative. So on the left hand side it's negative 3.27. And on the right hand side if we redistribute that negative we'd have negative five minus um a negative times a negative is plus the square to three and we can rewrite that as the squared of three minus five. And look that was the same thing, negative 3.27 and squared of three minus five. That was the same thing we had inside the absolute value brackets here we know those two are the same thing. So we look at our answer choices and that gives us answer choice. C well done, we'll catch you in the next one

Rewrite each expression without the absolute value bars. |√2-1|

Key Concepts

Absolute Value

Square Root

Piecewise Functions

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