Can anyone please tell me how I can manually calculate the answer to the following equation: My lesson only shows me how to do it on a scientifc calculator.

(2)^0.2

Thanks!

Guest Dec 6, 2014

#2**+10 **

There are actually some ways you can perform "difficult" computations on a very basic calculator. I'll show one such *numerical method *that happens to work really well for this specific problem.

Melody showed you are wanting to solve a×a×a×a×a = 2

We can re-arrange this as: solve a×a×a×a = 2/a

This can be written more concisely as: solve a^4 = 2/a

➤Remember, we are wanting to find the value of a

If we take two square roots of each side, we have an expression for a:

$$a = \sqrt{\sqrt {\dfrac a 2}}$$

Now for the fun part! Just guess a value for a, make it a reasonable guess. Then evaluate the right-hand expression using the value you guessed. If your guess was spot on, then the expression will evaluate to exactly the value of a you guessed, but hoping you'd guess correct to a few decimal places is really expecting too much. Once you have evaluated the right hand expression, use the result as a new value of a and re-evaluate the right hand expression.

Keep on doing that until the answers start to agree as closely as you'd like them to.

You are lucky because this exercise works really well with not a lot of work. You can test how close your final answer is my multiplying it by itself five times and seeing how close to 2.000 the result is.

I made my first guess 1.2, and this means the right hand side evaluates to 1.136

Now, using 1.136 for the value of a on the right hand side, it evalutes to 1.152

Now, use 1.152 ....... keep going ....

Good mathematics fun, isn't it!

Guest Dec 6, 2014

#1**+10 **

$$(2)^{0.2} = \sqrt[5]{2}$$

This means, what multiplied by itself 5 times =2

that is find $$a$$ if $$a\times a\times a\times a\times a=2$$

This is too difficult to do by hand. You need to use a calculator.

Even then it will be an approximation because this will be an irrational number. The digits will go on for ever.

Melody
Dec 6, 2014

#2**+10 **

Best Answer

There are actually some ways you can perform "difficult" computations on a very basic calculator. I'll show one such *numerical method *that happens to work really well for this specific problem.

Melody showed you are wanting to solve a×a×a×a×a = 2

We can re-arrange this as: solve a×a×a×a = 2/a

This can be written more concisely as: solve a^4 = 2/a

➤Remember, we are wanting to find the value of a

If we take two square roots of each side, we have an expression for a:

$$a = \sqrt{\sqrt {\dfrac a 2}}$$

Now for the fun part! Just guess a value for a, make it a reasonable guess. Then evaluate the right-hand expression using the value you guessed. If your guess was spot on, then the expression will evaluate to exactly the value of a you guessed, but hoping you'd guess correct to a few decimal places is really expecting too much. Once you have evaluated the right hand expression, use the result as a new value of a and re-evaluate the right hand expression.

Keep on doing that until the answers start to agree as closely as you'd like them to.

You are lucky because this exercise works really well with not a lot of work. You can test how close your final answer is my multiplying it by itself five times and seeing how close to 2.000 the result is.

I made my first guess 1.2, and this means the right hand side evaluates to 1.136

Now, using 1.136 for the value of a on the right hand side, it evalutes to 1.152

Now, use 1.152 ....... keep going ....

Good mathematics fun, isn't it!

Guest Dec 6, 2014