A Nice Algebra Maths Simplification | No Calculators Allowed

Added: 2026-05-28

[00:00:00]Hello. You're welcome to solve this math problem, which is square root of 81 power of 6 minus 81 power of 5.

[00:00:11]Now, solution. Into here, it will be equal to square root of 81 power of 6 to have 81 power of 5.

[00:00:19]81 power of 6 is same as 81 power of 6.

[00:00:22]It is power of 5 plus 1. Then minus 81 power of 5.

[00:00:29]Then from here, 81 power of 5 plus 1 is in the form of a power of m plus n, which is equal to a power of m times a power of n. So, we'll apply this form.

[00:00:43]Then it will be equal to square root of 81 power of 5 plus 1 is same as 81 power of 5 times 81 power of 1. Then minus this, 81 power of 5.

[00:00:59]Then into here, it will be equal to square root.

[00:01:03]From here, 81 power of 5 is common. So, we take 81 power of 5 outside the bracket.

[00:01:10]81 power of 5 times 81 power of 1 divided by 81 power of 5, it is this.

[00:01:15]81 power of 1. Then minus 81 power of 5 divided by 81 power of 5, it is 1. Bracket.

[00:01:24]Then into here, it will be equal to square root of 81 power of 5. Then times from here, 81 power of 1 is same as 81.

[00:01:37]So, here it will be 81 minus 1. It is 80.

[00:01:43]Then in the next step, here we separate the square roots. So, it will be equal to square root of this 81 power of 5 times square root of 80.

[00:01:57]Then into here, it will be equal to square root of 81 power 5 is same as 81 power of 4 + 1. Then times this square root of 80.

[00:02:11]Then here, it will be equal to square root of 81 power 4 + 1 is in this form.

[00:02:18]Then we change into this form. So here, it will be 81 power of 4 * 81 power of 1.

[00:02:27]Then times square root of 80 is same as is same as 16 square root of 16 * 5 is 80.

[00:02:38]Then here, it will be equal to we separate the square roots here. So it will be square root of 81 power of 4 * square root of 81 power of 1, which is same as square root of 81.

[00:02:52]Then times here, we separate the square roots. So it will be square root of 16 * square root of 5.

[00:03:01]Then into here, it will be equal to square root of 81 power 4 is same as square root of 81 power of 4 is same as power of 2 * 2.

[00:03:12]Then times square root of 81, it is 9 * square root of 16, it is 4. Then times this square root of 5.

[00:03:22]Then here, it will be equal to square root of 81 square * square is same as 81 power of 2 then bracket square. Then times 9 * 4, it is 36 times this square root of 5.

[00:03:42]Then into here, this square root will cancel square. So it will be 81 square.

[00:03:48]Then times 36 square root of 5.

[00:03:53]Then into here, it will be equal to Here 81 square is same as 80 plus one 81. Then bracket this square. Then times 36 square root of five.

[00:04:09]Then here it will be equal to we expand this so it will be 80 square.

[00:04:15]Then plus one square.

[00:04:18]Then plus two times 81 times one. Then here bracket the expansion of this. Then times times 36 square root of five.

[00:04:34]Then into here it will be equal to 80 80 square. 8 square is 64.

[00:04:41]Then double zeros plus one square it is one. Then plus two times 80 is 160 times one it is 160.

[00:04:52]Bracket then times 36 square root of five.

[00:04:58]Then here we find the sum of this inside the bracket. Zero plus one plus zero it is one.

[00:05:05]Six plus zero it is six.

[00:05:11]One plus four it is five.

[00:05:15]Then here it is six.

[00:05:18]Then times this 36 square root of five.

[00:05:25]Then into here it will be equal to 6561 bracket 36 is same as 30 plus six bracket this square root of five.

[00:05:39]Then here it will be equal to we multiply 30 times this here. Now zero Here 30 times this it is be zero. Then 3 * 1 it is three. 3 * 6 is 18, go with one.

[00:05:58]3 * 5 is 15 + 1 is 16, go with one. 3 * 6 is 18 + 1, it is 19.

[00:06:09]Then plus 6 * 1, it is six.

[00:06:15]6 * 6 is 36, go with three.

[00:06:19]6 * 5, it is 30 + 3 is 33, go with three.

[00:06:24]6 * 6 is 36. Plus three, it is 39.

[00:06:30]Then bracket this square root of five.

[00:06:35]Then into here, we'll find the sum here inside the bracket. So, it will be 6 + 0, it is six.

[00:06:41]6 + 3, it is nine.

[00:06:44]3 + 8, it is 11, go with one.

[00:06:48]Then 9 + 6 is 15 + 1 is 16, go with one.

[00:06:55]3 + 9 is 12. Plus one, it is 13, go with one.

[00:07:02]Then 1 + 1, it is two. This here square root of five.

[00:07:08]So, this here is our final answer.

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[00:07:23]Bye-bye.