This square root question looks impossible.

the denominator tells you exactly what What to do next? Welcome back to my channel, so because the the denominator is a sword, right? That means I need to rationalize this first, so let's rationalize rationalize now to do that we need to write this as the square root 64 divided by 8 plus 63 They are going to multiply the numerator. and multiply both the numerator and the denominator by the conjugate of our denominator and the conjugate of this is 8 minus square root of 63, 8 minus square root of 63. Now, if we move forward, we can now write this as the square root. of 64 brackets 8 minus root 63 divided by 8 plus root 63 multiplied by 8 minus root 63 now if you look at the denominator it is in the form a plus b multiplied a minus b means that we can express this as what a squared minus b squared: difference of two squares so that's exactly what we are going to So we will write this as The Scare Root of 64 brackets 8 minus root 63 divided by 8 squared minus 63 square if this is the first time you've seen Please click the subscription button for this channel. Turn on your notification bell so that you don't miss our videos, we upload our videos as often as possible to tune in at your convenience, there must be something new for you to watch and give us a Thumbs up if you love what we are doing and most importantly, please drop down your comments here Good, the bad, the ugly—tell me what you feel about my video and how I need to improve Thank you very much. And if there is a shorter way to solve this, Please don't hesitate to also mention that in the comments. So moving forward, we can now write this as the square root of 64 brackets, 8 minus 63, divided by, now we have 8 squared is 64, minus. Now the square cancels the square roots, and we have 63. That means we have reduced this to the square root. of 64 brackets 8 minus root 63 right because this becomes one Okay, now recall that recall. the square root of a multiplied by p can can be expressed as the square root of a multiplied by the square root of b that we can write this as a square root 64 multiplied by square root of 8 minus the square root of 63, so if we Then this becomes 8 brackets the square root 8 minus the square root of 63 and we can go ahead right and say that this is equal to 8 square root of Now we are going to write this as 1 multiplied by what? 8 minus root 63, we have not changed everything anything divided by one is one over one We haven't changed anything, and we can write this as eight fruits. Then we can change one to two. eight times the square root of 63 divided by two because when it divides itself we have one we haven't changed anything yet either You're going to see why I'm doing this. Yes. So, stay put and see why. I'm going to explain later. So, solving this, let's expand the parentheses. We have 8 times the square root of 2 times 8. Is 16 minus 2 times the square root of 63 divided by 2? If we solve for that, we can write this as 8 square root of Now 16 is the same as 9 plus 7, right, like I said you you are going to see why I introduced these two Okay, so 16 is 9 plus 7 multiplied by 2 roots. and 63 is 9 times 7 so 9 times 7 divided by 2, have you Subscribed if you haven't already; I think this is the right time. to do that so you don't forget We can write this as eight roots now nine can can be expressed as three squared, right three squared plus seven can be written as square root seven squared square root of seven squared then we have multiplied by, is that supposed to to be subtraction, sorry, not multiplication by So minus root 9 times root 7, right? Now, everything divided by 2. Let me come to this side. Now, we can write this as 8 square root. 3 squared plus square root 7 squared minus 2 multiplied by, The square root of 9 is 3, multiplied by the square root of 7, now divided by 2. This is where I explain why I did what I did. This is the reason. Remember that a squared plus b squared minus two a b is the same thing (a minus b) squared, right, and you can see that I have arranged this numerator in this form whereby My a is three and my b is seven, right? Therefore, let's go ahead and write. our new simplified equation, so this becomes eight So, this becomes 3 minus root 7. all squared divided by 2, okay? Excuse me. This is equal to 8. Then I can write this as the square root of 3 minus 7 divided by the square root of 8 Sorry, the square root of 2 rather. And here, this, and this—so we have eight. three minus the square root of seven, divided by the square root of two Now remember that we cannot leave this root two No, so we need to rationalize the denominator. by multiplying the numerator and multiply the denominator by this, so we have multiplied by root two multiplied by root two, okay, so now we have eight root two Bracket 3 minus root 7 divided Root 2 times root 2 is 2. If we divide this, We have 4 root 2 times (3 minus root 7). If we expand this further, we can write it as 4 times the square root of 2 multiplied by 3. is 3 root 2 minus root 7 times root 2. What do we give ourselves? Root 14. And that's the answer. Thank you for watching. See you in my next video, bye.