Learn about Roots Applications In this lesson, let's learn how to apply the concept of roots and square roots to real life. The problem we’re givens ays the following. Julie wants to plant a square garden of wildflowers. She has enough wildflower seed to cover 19 square feet. So she's going to plant a square garden. The area of which is 19 square feet. Estimate to the nearest tenth the side length of a square. We need to find this length. What's the area? The area is length x length or 19 square feet which is the area is length squared or length equals square root of 19 square feet or whatever that value is. So in order to find L to the nearest tenth, we need to compute the root of 19. Well, here is the way we compute the root of 19. Let's take some estimates. Let's check what is 4.22. Why are we checking 4.2? Because square root of 19, if I look at what’s closest to it, it's 16 and 25 are the two perfect squares. 42 is 16 and 52 is 25. So if I want to find the value tat when multiplied to itself gives me 19, I'm looking for a value between four and five because 42 is too less, 52 is too much. So the value is going to be somewhere four and five. So let's start with 4.2. Let's take a little bit of space. 4.22=4.2 x 4.2 which is 17.64. Well, that is too low. Let's try 4.42; 4.42 which is 19.36. Well, that’s too high. So let's try 4.32, is 4.3 x 4.3 which is 18.49, closer but that is still too low. So I know the numbers between these two. So let's try 4.352. When I compute this, this is 18.9225. It's still a little low but I'm getting closer. So now I know the number is between 4.35 and 4.4. It's somewhere near because the square of this is here and square of this is 19.36. So if I know the numbers between these two and I have to find the number to the nearest tenth, well, the nearest tenth is 4.3 or 4.4. That’s the tenth value. Well, if it's that 35, it's going to round up to 4.4 anyway. If you rounded up anything greater than 4.35 to the nearest tenth, we would get 4.4. So, I might as well stop here and say that the area or the square root of 19, the estimate is 4.4. So what's the size that they're looking for? The side of the yard that Julie needs to plant is 4.4 feet. What we did was looked at what we are trying to compute which is the root of 19 and tried to take some estimates going above and below trying to get the closest. The closest I got was 4.3 multiplied by itself, 4.3 multiplied by itself gives me a pretty close number. The one higher than that is 4.4 which went over 19. So I knew the number have to be between these two. Since the question only wants me to calculate to the nearest tenth, I could just round up to 4.4 because no matter whether it will be 4.36, 4.37, 4.38, it wouldn’t make a difference because it would be rounded to 4.4 anyway because we’re rounding to the tenth digit or the tenth value digit.