Express the square root of 640 in the form 𝑎 root 𝑏, where 𝑎 and 𝑏 are integers and 𝑏 takes the least possible value.
In order to simplify the surd root 640, we need to consider the square numbers and which of these are factors of 640. In particular, we’re looking for the highest factor of 640 that is also a square number or perfect square.
In this case, the highest factor of 640 is 64. As 64 multiplied by 10 is 640, we can rewrite the square root of 640 as the square root of 64 multiplied by the square root of 10. The square root of 64 is equal to eight as eight multiplied by eight is 64. Therefore, we can simplify square root 64 multiplied by square root 10 as eight multiplied by root 10 or eight root 10.
To check whether 𝑏 has taken its least possible value, we need to look at our square numbers again. Apart from one, do any of the square numbers divide exactly into 10? Well, we know that four and nine are not factors of 10. And seen as all the other numbers are larger than 10, 10 is the lowest value or least possible value of 𝑏. This means that the simplest form of the square root of 640 is eight square root 10 or eight root 10.