WEBVTT
00:00:01.740 --> 00:00:08.240
Identify which of the arrows represents the position of the square root of 51.
00:00:09.230 --> 00:00:12.530
Square-rooting is the opposite of squaring a number.
00:00:12.890 --> 00:00:16.800
So it is worth writing out our square numbers first.
00:00:17.440 --> 00:00:23.050
Three squared is equal to nine, as three multiplied by three is nine.
00:00:23.630 --> 00:00:29.470
Four squared is equal to 16, as four multiplied by four is 16.
00:00:30.350 --> 00:00:41.930
The square of the integers from five to 10 are 25, 36, 49, 64, 81, and 100, respectively.
00:00:42.740 --> 00:00:48.920
As seven squared is equal to 49, the square root of 49 is equal to seven.
00:00:49.980 --> 00:00:53.490
In the same way, eight squared is equal to 64.
00:00:53.740 --> 00:00:56.950
The square root of 64 is equal to eight.
00:00:57.560 --> 00:01:02.410
51 is greater than 49 but less than 64.
00:01:02.930 --> 00:01:11.740
Therefore, the square root of 51 must be greater than the square root of 49 and less than the square root of 64.
00:01:12.690 --> 00:01:19.630
We can, therefore, say that the square root of 51 is greater than seven but less than eight.
00:01:20.580 --> 00:01:25.190
The only arrow that lies between seven and eight is arrow 𝑐.
00:01:26.110 --> 00:01:32.680
This means that the arrow that represents the position of the square roots of 51 is 𝑐.