Algebra simplification|No calculator.

First, let us simplify what we have here. I am going to solve this using two methods. So this particular one is the first method. Now, in the first method, we are going to What is this 30 sentences as? 10 times 3, right? raised to the power of 3 plus this sentence as 4 multiplied by 10 equals 40. raised to the power of 3 plus this sentence as 5 times 10 raised to the power of 3 What is it equal to? Now, we factorize. But before that, let's open this bracket. According to the law of indices, a multiplied by n raised to the power of b is equal to a to the power of b multiplied by n to the power of b. So we are going to use this or we are going to express this in this form. So, if we do that, then we have 10 to the power of 3 multiplied by 3 to the power of 3 4 to the power of 3 plus 4 multiplied by 10 to the power of 3 5 to the power of 3 plus 5 multiplied by 10 to the power of 3 What is it equal to? Now, let's go ahead and factorize. Because when you look at this, Notice that we have 10 to the power of 3. 10 to the power of 3 and 10 to the power of 3 So we are going to factorize it To simplify this particular question. So we do that right now. We are going to have 10 to the power of 3. We open our bracket. When this is divided by 10 to the power of 3, we have 3 to the power of 3 plus when this is divided by this, we'll have 4 to the power of 3 plus when this is divided by this, we'll have 5 to the power of 3. Okay. Now, this is equal to square root of 10 to the power of 3 multiplied by Remember that this is the first method. That we have two methods, right? We are going to use two methods to solve this. What is 3 to the power of 3? That is 3 times 3 times 3 And that's 27, right? So we have 27 plus What is 4 to the power of 3? Four times four is sixteen. 16 times 4 should be 64, right? So we have 64 Five to the power of three is 125. Okay. Now, let's move to this side. If this is the first time you are encountering this channel, Please don't forget to hit the subscription button and on your notification bell so that you'll be notified whenever I upload a new video. Thank you so much. So this is where we are. Let me copy it out. The square root of 10 to the power of 3 ctypes MATCH 27 64 plus 125. Perfect. Now, this is equal to square root of 10 to the power of 3 multiplied by Now let's add this. If we add, we have 125, 64, 27. Now, 5 plus this makes 9. And 9 plus 7 is 16. We carry 1. This will give us 10 Plus 1 is 11. Then we add 1 here. We have 216. 216 So this is the square root of 10 to the power of 3. multiplied by 216. Now, this is equal to The square root of what? 10 to the power of 3 Now, 216 is 6 to the power of 3, right? multiplied by 6 to the power of 3. Now, when you have the same power just as we did here, We are going to bring this into the bracket. And we're going to bring the 3 outside. So if we do that, we will have 10 times 6 raised to the power of what? 3. Now, this is equal to The square root of 16 raised to the power of 3. Now, we can express this as what? We can express this as square root of 16 squared multiplied by 16 to the power of 1. Using the law of exponents, we have that a to the power of m multiplied by a to the power of n is equal to a to the power of m plus n. That is why we can express this as that. Now, let's continue. So, we can now open this bracket or we can distribute this square root sign For both of them. So, we have the square root of 16 squared. multiplied by the square root of 16 Alright, let's continue from here. If we do that, then we have Now, the square root of 16 squared Will give us 16, right? So, we have 16 here. So, 16 multiplied by the square root of 16, right? Square root of 16. Now, this is equal to 16 multiplied by Now, 16 is the same as 4 times 15. 4 multiplied by 15 equals 60. Now, this is equal to 16 multiplied by So, this is the same thing as the square root of 4. multiplied by the square root of 15, right? Now, this is 16 multiplied by The square root of 4 will give us 2. multiplied by the square root of 15. So, this is equal to 120 root 15. That concludes the first method. Now, let's use the second method. Now, let's move on to the second method. That is method 2. So, this is equal to the square root of Now, 30 to the power of 3 simply means 30 plus 30 times 30 Sorry, 30 times 30 times 30 which will give you 3 times 3 times 3 I'll give you 27. And we have three zeros, right? 1, 2, 3. So, that means this is 27,000. So, we have 27,000 plus, similarly, 40 times 40 times 40. We are going to have three zeros. Then, 4 to the power of 3, which is 64, right? So, we have 64,000 Besides, here we are going to have three zeros. And 5 to the power of 3 is 125. So, 125,000. Okay. Then, we go ahead. If you add this together, What are you going to have? We are going to have 216,000 because we have added something similar to it before. Right? Now, this is equal to the square root of 1,000. multiplied by 216. So, this is equal to square root of 10 to the power of 3 multiplied by 6 to the power of 3 Now, if we continue, we have What is the square root of this? 10 times 6 raised to the power of 3. Okay. So, this is equal to cube root of 60 which is equal to square root of 60 squared multiplied by 60 which is equal to square root of what? Square root of 60 squared multiplied by the square root of 60. Okay. So, we divide this. We are left with 60 multiplied by square root of 4 times 15 So, this is 60 multiplied by This is 2 root 15, right? And which will still give us the same answer which is 120 root 15. Thank you so much for watching. Have a lovely day.