Math Olympiad | How to solve this square roots radical math olympiad question |

[00:00:00]Hello everyone. Welcome to Rasha's Classroom. Today we are solve a interesting radical math question.

[00:00:06]Square root down a square root a square root a * square root a is equal to 7. a is equal to what? How to solve this interesting square root 8 grade question? Our math solution, it is a easy math problem.

[00:00:25]First of all, I take our question which is a square root down a, then again I take here is a square root a, then this is a square root a, and this is a square root a is equal to 7. This is our question.

[00:00:43]First of all, I take both side whole square. I take here is a square, then I take here is a square.

[00:00:50]Now, at this moment you can say this a square root and this a square is cancel.

[00:00:55]We find out it will be a, then here is a square root. This is a, and this is a square root this a, then this is a square root a is equal to 7 to the power 2.

[00:01:10]Now, I want to remove this a square root again. So, at this moment I use both side whole square again. So, this is a, and this is a square root a, and this is a square root a, then again a square root a bracket power is 2. I use both side whole square again. This is 7 to the power 2 bracket power is 2.

[00:01:36]I solve this interesting a square root math problem step-by-step.

[00:01:41]Then this is a to the power 2. So, this is a to the power 2 times and this is a square root this a times this is a square root this a times this is a square root this a bracket power is two. I mean this two is equal to seven to the power four. We know that two times two I put on the exponential formula it will be four.

[00:02:08]Then this is a to the power two.

[00:02:11]Then this square root and this square is cancelled. This is a times and this is square root a this a and this is square root a is equal to seven to the power four.

[00:02:29]Then at this moment I put on the exponential formula I add this exponent because of that here is base is same. So this is a to the power two plus one this is three.

[00:02:39]So this is a cube and this is square root a and this is a square root a is equal to seven to the power four.

[00:02:50]Now I want to remove this square root.

[00:02:52]So I use both side again whole square.

[00:02:55]You can solve this question others method because of that we know that a square root a is equal to a to the power one over two. You can solve this question like this method.

[00:03:06]Now this is a to the power three. I take this a to the power three bracket power is this two.

[00:03:13]Then this is a square root a times square root a and bracket power is two is equal to this is seven to the power four times two this is eight.

[00:03:28]Then this is a to the power six because of that three times two this is six. But this is square root and this is square is cancelled. This is a square root a is equal to seven to the power eight.

[00:03:42]Now at this moment you can say this is a to the power seven because of that this exponent is one. One plus six this is seven and this is a square root a is equal to seven to the power eight.

[00:03:57]Now, I want to remove this square root again. So, this is a to the power seven.

[00:04:03]And this is a square root a and I use both side whole square again. And this is seven to the power eight.

[00:04:12]Then, this is a to the power seven.

[00:04:15]Power is two. So, I take this a to the power seven and bracket power is two.

[00:04:20]And I take this a square root a bracket power is two. This two. And this is seven to the power eight. And I take here is whole square.

[00:04:32]This is square and then I take this is square. So, it will be seven to the power 16.

[00:04:38]Now, at this moment you can say this is a to the power seven times two. This is 14.

[00:04:45]And this is square root is cancelled.

[00:04:49]This is a. Then, this is seven to the power 16.

[00:04:54]Now, according to exponential formula you can say this expression it will be a to the power 14 plus one. This is 15.

[00:05:03]And is equal to seven to the power 16.

[00:05:08]Here is a is equal to what? How to simplify this exponential expression?

[00:05:13]How to solve for a this exponential equation? So, you can say this is a to the power 15.

[00:05:19]And I take both side one over 15.

[00:05:23]Then, this is seven to the power 16.

[00:05:25]I take both side one over 15.

[00:05:28]Now, this 15 this 15 cancel out. We have find out our final answer. A is equal to seven to the power 16 over 15. This is our final answer in this radical math question. This is the below of a in this is square root math olympiad question. Thank you all. If you enjoyed this math problem, please subscribe my channel for other interesting video.

[00:05:54]Goodbye. Take care everyone. Have a good day.