Estimate the value of root 4.87 multiplied by 2.15 minus 3.09.
The keyword of this question is actually the word “Estimate” because if it says to estimate, that means that you must do that. You can’t work out the exact value as you will not get the marks. You need to show you can round an estimate to a sensible degree. Like I said, the most common mistake is that students will work out the exact value, but that won’t get you the marks.
Okay, so when we’re going to estimate, what we actually do is we round each of the numbers to one significant figure. So what we’re gonna do is actually do them each in turn. So we’re gonna start with 4.87. So if we want to round 4.87 to one significant figure, then the first significant figure is going to be four. Then, I’ll look at the number after four, which is eight. Because this eight is actually higher than five or five or higher, then therefore we’re actually gonna round the four up. So therefore, 4.87 is equal to five to one significant figure.
Okay, let’s move on to 2.15. Again with 2.15, we’ll look at the first significant figure, which is two. Then, we have got a number after it, which in this case is one. And as this is less than five, then the two will stay the same. So therefore, 2.15 is equal to two to one significant figure.
And then, finally, we’re gonna move on to 3.09. So we look at the first number again, which is our three. So it’s the first significant figure. Then, after that, we have a zero. So therefore, the three stays the same. So we can say 3.09 is equal to three to one significant figure.
Okay, great, so now we’ve actually rounded each of the values. Let’s put them back into our square root. So now, what we have is the square root of five multiplied by two minus three, which is gonna give us the square root of 10 minus three. That’s because because of BODMAS or BIDMAS, we did the multiplication first. So five multiplied by two is 10. So we’re gonna have the square root of 10 minus three, which would give us an answer of root seven.
Okay, great, but this actually isn’t the value that we’re looking for at the end. So what we do now? How to actually estimate what root seven is going to be? Well, what we think is, “well, which two square numbers is seven between?” So we can get well, seven is between four and nine because it’s greater than four which is a square number and it’s less than nine which is the next square number.
So therefore, if we actually take the square root of each section of our inequality, we’re gonna get root four is less than root seven is less than root nine. And therefore, if we actually work out what these are, well, root four is equal to two and root nine is equal to three, so therefore we can say that our answer for our estimation is between two and three because we can see that root seven is greater than two, but less than three.
So what we do to actually make our final estimate? Well, what we actually do is we say, “okay, we’ll say that root seven is between these two values.” So we can say that root seven is approximately equal to 2.5. So therefore, what we can say is that if we estimate the value of the square root of 4.87 multiplied by 2.15 minus 3.09, we can say that it’s approximately equal to 2.5.