Video Transcript
Determine the value of 𝑥 squared, given that 𝑥 is equal to eight root 10.
Well, if we look at 𝑥 squared, this means 𝑥 multiplied by 𝑥. So therefore, 𝑥 squared is gonna be equal to eight root 10 multiplied by eight root 10. And this is because 𝑥 is equal to eight root 10. Okay, so how do we calculate eight root 10 multiplied by eight root 10? Well, the easiest way to deal with this is to first of all multiply the eights together. So you have eight multiplied by eight. Then you multiply this by root 10 multiplied by root 10. So we’ve just split it up. And we do this cause, first of all, we’ve got 64. And 64 is equal to eight multiplied by eight.
Now for the second part, what we’re gonna use is one of our radical or surd laws. That is that if we have root 𝑎 multiplied by root 𝑎, then we just get 𝑎. So therefore, if we have root 10 multiplied by root 10, we’re just gonna have 10. And this is one of the rules we should remember. But let’s look at why this works as well. Well to help us understand why it works, we can look at another one of our radical or surd rules. And that is if we have root 𝑎 multiplied by root 𝑏 is equal to root 𝑎𝑏.
So therefore, if we have root 10 multiplied by root 10 we’re gonna have root 100. And that’s because 10 multiplied by 10 is 100. And if we’ve got root 100, then the square root of 100 is actually 10. And that’s because, as we said, 10 multiplied by 10 is 100. Okay, great, so we’ve got 64 multiplied by 10. So therefore, we can say that the value of 𝑥 squared, given that 𝑥 is equal to eight root 10, is gonna be equal to 640. And that’s because 64 multiplied by 10 is 640.
