### Video Transcript

Michael is trying to find which two
whole numbers lie on either side of the square root of 51. He decides that it will be helpful
to use what he has been taught about square numbers. What is the greatest square number
below 51? What is the smallest square number
above 51? Hence, determine the two
consecutive whole numbers that the square root of 51 lies between.

First of all, we should think about
what we know about square numbers. A square number is the result of
multiplying an integer by itself. For example, one squared is one,
and two squared is four. So, we call four a square
number. It’s helpful to memorize the first
10 or so square numbers. Three squared is nine. When we’re listing out square
numbers, the first three are one, four, nine, then four squared, which is 16, five
squared, which is 25, six squared, which is 36, seven squared, which is 49, eight
squared, which is 64, then 81, and then 100. These are the first 10 square
numbers, and we can use that to answer the questions below.

What is the greatest square number
below 51? This means we’re looking for the
square number that’s closest to 51 but not over. And that’s gonna be 49. The next question is similar. What is the smallest square number
above 51? That means we need the square
number that’s closest to 51 but must be greater than 51. And here, that’s going to be
64. If we put 49 and 64 on a number
line, 51 would fall between them but closer to 49.

Now, on another number line, we
could put the square root of 49 and the square root of 64. Again, when we add the square root
of 51, it falls closer to the square root of 49 than it does to the square root of
64. But we know that the square root of
49 is seven, and the square root of 64 is eight. Which means we can say that the
square root of 51 will fall somewhere between the consecutive whole numbers of seven
and eight.