In this lesson, we’ll use the number line to find square roots. We need to find the letter that identifies a position of each of the square roots given here and we’re given five letters. Let's do them one by one.
Part A, we need to find the negative square root of three, the negative square root of three. Here’s how I'm going to do it. We’re going to find a value, a perfect square that is close to three. What's the number which is a perfect square that is closest to three while on the higher side that number is four, two square is four and the lowest carried it’s one. One squared is less than three, is less than two squared as you can see.
Now, let's do the square root for each one of this. Square root of three is less than square root of two squared is two and square root of one squared is one. So, square root of three lies between two and one. But we’re interested in the negative square root, so negative square root of three lies between negative one and negative two but I reversed the inequalities because negative root of three lies between negative one and negative two but negative two is actually less than negative one. Two is greater than one, always remember to do is reverse the inequalities.
So, now that we have this, we can see that the value that we were looking for lies between negative one and negative two which is where? That’s right here. So, the answer to this is B.
Let's try Part B which is root of five. Again root of five, I'm going to take five and figure out. Let’s take five and figure out a number that is less than and greater than five that is a perfect square. Well, here it’s nine, here it’s four. That’s two squared and three squared. So, the root of five is between two and three, two squared is four, three squared is nine. So, root of five which is what we’re looking for square root of five should lie between two and three whereas between two and three. That’s D and E, any of this could be the number. But now let’s look at is five closer to four or closer to nine? Well, five is closer to four so the root of five will be closer to two. So, D must be the answer.
Let’s try Part C, I'm going to scroll down a little bit. Part C is root of seven. Again, if I take seven that’s between nine and four as well, which means root seven lies between three and two but seven is closer than nine. So, root seven is closer to three. Closer to three, that is our number right here, that’s E. Now, let's look at root of 0.75. The root of 0.75, if I take 0.75 that lies between perfect squares zero and one. Root of 0.75 lies between square root of one is on, square root of zero is zero. So, we are interested in a point which is between zero and one. That’s right, that’s between zero and one as point here. So, the answer to this is point C.
Notice that we basically applied the same concept. We took the value that was given to us, looked at the number inside the square root and try to find perfect squares that were just above and just below that number. Once we had that, we took the square roots of this all three to find that this value would lie between two and three. Between two and three that’s the value we were looking for. Okay, so what have we learned? I can use the number line to find the square roots of different digits right if that’s what we wanted to do.
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