WEBVTT
00:00:01.560 --> 00:00:05.680
A square number and a prime number have a total of 22.
00:00:07.040 --> 00:00:08.560
What are the two numbers?
00:00:11.360 --> 00:00:18.960
In this problem, we’re told that the total of a square number and a prime number is 22.
00:00:20.680 --> 00:00:27.120
To work out what the two numbers are, we need to remember what a square number is and what a prime number is.
00:00:28.680 --> 00:00:34.040
A square number is formed by multiplying a number by itself.
00:00:35.600 --> 00:00:39.240
Let’s find as many square numbers as we can that are less than 22.
00:00:40.520 --> 00:00:46.040
One squared has a value of one multiplied by one, which is one.
00:00:47.000 --> 00:00:48.600
So one is a square number.
00:00:50.080 --> 00:00:52.800
Two squared is the same as two multiplied by two.
00:00:53.720 --> 00:00:56.000
So the next square number is four.
00:00:58.040 --> 00:00:59.800
Three squared equals nine.
00:01:01.720 --> 00:01:03.880
And four squared equals 16.
00:01:05.440 --> 00:01:08.360
Five times five is 25; so that’s too large.
00:01:09.440 --> 00:01:17.760
The only square numbers that could feature in our calculation are: one, four, nine, or 16.
00:01:19.160 --> 00:01:22.880
But what are the pairs that go with these numbers to make 22?
00:01:24.040 --> 00:01:35.760
One plus 21, four plus 18, nine plus 13, and 16 plus six.
00:01:35.760 --> 00:01:40.160
Now we need to ask ourselves, which of these second numbers are prime?
00:01:41.320 --> 00:01:42.760
What is a prime number?
00:01:43.920 --> 00:01:54.680
A prime number is a number with exactly two factors, one — well, all whole numbers have a factor of one — and itself.
00:01:56.000 --> 00:01:59.520
Let’s go through the factors of each of our numbers to see which one is prime.
00:02:00.800 --> 00:02:07.640
The factor pairs that make 21 are one times 21 and also three times seven.
00:02:09.040 --> 00:02:13.400
21 has four factors; so we know it’s not prime.
00:02:14.520 --> 00:02:16.920
The pair of numbers we’re looking for can’t be these two.
00:02:18.560 --> 00:02:20.640
How many factors does 18 have?
00:02:21.680 --> 00:02:31.280
The factor pairs that make 18 are one and 18, two and nine, and also three and six.
00:02:32.240 --> 00:02:34.400
18 has six factors.
00:02:35.080 --> 00:02:36.560
So we know that’s not prime either.
00:02:37.560 --> 00:02:40.000
There’s only one multiplication that makes 13.
00:02:40.920 --> 00:02:42.560
And that’s one times 13.
00:02:43.440 --> 00:02:45.400
13 is a prime number.
00:02:46.120 --> 00:02:52.640
It has exactly two factors, one and itself, which is 13.
00:02:55.320 --> 00:02:58.000
So it looks like we’ve found our square number and prime number.
00:02:58.680 --> 00:03:01.040
Let’s just check that six isn’t a prime number.
00:03:02.040 --> 00:03:07.640
Six has four factors: one, two, three, and six.
00:03:08.440 --> 00:03:10.080
And so we know it’s not prime.
00:03:12.080 --> 00:03:14.840
The pair of numbers are nine and 13.
00:03:15.960 --> 00:03:19.200
We started off by reminding ourselves what a square number is.
00:03:20.000 --> 00:03:24.720
And then finding all the square numbers that we could add another number to, to get to twenty-two.
00:03:25.960 --> 00:03:31.720
We then worked out what the pairs were, what number we needed to add to the square numbers to make 22.
00:03:32.960 --> 00:03:35.560
And so we needed to find out which one of these was prime.
00:03:36.320 --> 00:03:38.960
We reminded ourselves what a prime number was.
00:03:40.160 --> 00:03:46.960
And then we went through each number to find out which one only had two factors, one and itself.
00:03:48.200 --> 00:03:51.640
A square number and a prime number have a total of 22.
00:03:53.120 --> 00:03:58.960
The square number is nine and the prime number is 13.
00:04:00.080 --> 00:04:03.680
Nine plus 13 equals 22.