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## #1 2023-11-12 14:53:22

sologuitar
Member
Registered: 2022-09-19
Posts: 467

### Square Root Raised to Square Root

How do you solve a square root raised to another square root?

What is sqrt{2}^(sqrt{2})?

Let me see.

Should I rewrite sqrt{2} as x^(1/2)?

[x^(1/2)]^(x^(1/2))

(1/2)(x^(1/2) = (x^(1/2))/(2)

I now get x^[(x^(1/2))/(2)].

You say?

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## #2 2023-11-13 04:41:05

Bob
Administrator
Registered: 2010-06-20
Posts: 9,863

### Re: Square Root Raised to Square Root

This shouldn't have an 'x' in it. 1.414^1.414 ≈ 1.6225

Bob

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

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## #3 2023-11-13 04:48:25

e_jane_aran
Member
Registered: 2023-09-15
Posts: 10

### Re: Square Root Raised to Square Root

harpazo1965 wrote:

How do you [evaluate or simplify] a square root raised to another square root?

What is sqrt{2}^(sqrt{2})?

Use technology to obtain a decimal approximation. That is, use your calculator or an online resource such as Wolfram Alpha:

https://www.wolframalpha.com/input?i2d=true&i=Power%5B%5C%2840%29Sqrt%5B2%5D%5C%2841%29%2CSqrt%5B2%5D%5D

"They are fast. Faster than you can believe. Don't turn your back. Don't look away. And most of all, don't blink." -the 10th Doctor

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## #4 2023-11-13 13:51:13

sologuitar
Member
Registered: 2022-09-19
Posts: 467

### Re: Square Root Raised to Square Root

Bob wrote:

This shouldn't have an 'x' in it. 1.414^1.414 ≈ 1.6225

Bob

Another problem found online. I am not in the business of making up my own problems. I try solving problems created by others, particularly math teachers.
I have 2 math textbooks. I  going to buy a Calculus textbook that covers Calculus l, ll, and lll for future self-study. In fact, I will purchase one this coming payday.

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## #5 2023-11-13 13:52:40

sologuitar
Member
Registered: 2022-09-19
Posts: 467

### Re: Square Root Raised to Square Root

e_jane_aran wrote:
harpazo1965 wrote:

How do you [evaluate or simplify] a square root raised to another square root?

What is sqrt{2}^(sqrt{2})?

Use technology to obtain a decimal approximation. That is, use your calculator or an online resource such as Wolfram Alpha:

https://www.wolframalpha.com/input?i2d=true&i=Power%5B%5C%2840%29Sqrt%5B2%5D%5C%2841%29%2CSqrt%5B2%5D%5D

Copy. Will do. Is there an algebraic way to simplify this stuff?

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## #6 2023-11-14 04:14:23

amnkb
Member
Registered: 2023-09-19
Posts: 175

### Re: Square Root Raised to Square Root

e_jane_aran wrote:

Use technology to obtain a decimal approximation. That is, use your calculator or an online resource such as Wolfram Alpha:

https://www.wolframalpha.com/input?i2d=true&i=Power%5B%5C%2840%29Sqrt%5B2%5D%5C%2841%29%2CSqrt%5B2%5D%5D

sologuitar wrote:

Is there an algebraic way to simplify this stuff?

don't think so
if wolfram alpha cant come up with an exact ans then you and me probably cant either

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## #7 2023-11-14 10:33:36

sologuitar
Member
Registered: 2022-09-19
Posts: 467

### Re: Square Root Raised to Square Root

amnkb wrote:
e_jane_aran wrote:

Use technology to obtain a decimal approximation. That is, use your calculator or an online resource such as Wolfram Alpha:

https://www.wolframalpha.com/input?i2d=true&i=Power%5B%5C%2840%29Sqrt%5B2%5D%5C%2841%29%2CSqrt%5B2%5D%5D

sologuitar wrote:

Is there an algebraic way to simplify this stuff?

don't think so
if wolfram alpha cant come up with an exact ans then you and me probably cant either

Again, just a question. No need to belittle anyone for asking questions that maybe others are hesitant to ask.

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## #8 2023-11-14 13:09:53

amnkb
Member
Registered: 2023-09-19
Posts: 175

### Re: Square Root Raised to Square Root

sologuitar wrote:

Is there an algebraic way to simplify this stuff?

amnkb wrote:

don't think so
if wolfram alpha cant come up with an exact ans then you and me probably cant either

sologuitar wrote:

Again, just a question. No need to belittle anyone for asking questions that maybe others are hesitant to ask.

i was just admitting that i'm not that good at math
being honest abiout my limitations
i didn't mean to 'belittle' myself
trying to stay humble
or was it the smily that offended you?
either way, sry

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## #9 2023-11-14 14:54:12

sologuitar
Member
Registered: 2022-09-19
Posts: 467

### Re: Square Root Raised to Square Root

amnkb wrote:
sologuitar wrote:

Is there an algebraic way to simplify this stuff?

amnkb wrote:

don't think so
if wolfram alpha cant come up with an exact ans then you and me probably cant either

sologuitar wrote:

Again, just a question. No need to belittle anyone for asking questions that maybe others are hesitant to ask.

i was just admitting that i'm not that good at math
being honest abiout my limitations
i didn't mean to 'belittle' myself
trying to stay humble
or was it the smily that offended you?
either way, sry

There is always a way to solve problems without a calculator.
Perhaps advanced techniques are needed.

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## #10 2023-11-14 17:47:16

amnkb
Member
Registered: 2023-09-19
Posts: 175

### Re: Square Root Raised to Square Root

sologuitar wrote:

There is always a way to solve problems without a calculator.

i wish, but no
thats why we need 'numerical analysis'
it has ways to solve things numerically/approximately
article - ask a mathematician
specific example - stack overflow
sry

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## #11 2023-11-14 18:15:17

sologuitar
Member
Registered: 2022-09-19
Posts: 467

### Re: Square Root Raised to Square Root

amnkb wrote:
sologuitar wrote:

There is always a way to solve problems without a calculator.

i wish, but no
thats why we need 'numerical analysis'
it has ways to solve things numerically/approximately
article - ask a mathematician
specific example - stack overflow
sry

Numerical analysis is an advanced course.

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## #12 2023-11-14 21:29:43

Bob
Administrator
Registered: 2010-06-20
Posts: 9,863

### Re: Square Root Raised to Square Root

There is always a way to solve problems without a calculator.

Before calculators some answers could only be obtained by doing the 'sums' long hand or by estimating or by using a tool such as a slide rule or logs.  What I mean is there will be problems which won't simplify to a simple answer.

B

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

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## #13 2023-11-16 18:06:16

sologuitar
Member
Registered: 2022-09-19
Posts: 467

### Re: Square Root Raised to Square Root

Bob wrote:

There is always a way to solve problems without a calculator.

Before calculators some answers could only be obtained by doing the 'sums' long hand or by estimating or by using a tool such as a slide rule or logs.  What I mean is there will be problems which won't simplify to a simple answer.

B

Thank you, Bob. In that case, thank God for calculators.

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## #14 2023-11-17 15:46:09

KerimF
Member
From: Aleppo-Syria
Registered: 2018-08-10
Posts: 53

### Re: Square Root Raised to Square Root

May I add...

The main difficulty in solving a practical problem is to find the formulas/equations which will lead, usually by using math tricks, to the end values to be applied for a certain project.

We are fortunate now that, for solving an equation or formula, there are many numerical tools (likely PC programs), to choose from, which help us find the numerical answer(s) we are looking for.

For instance, solving a new problem whose formulas/equations are not known yet by humans, even the most intelligent robot cannot do it. Otherwise, humans will be no more needed in research departments

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## #15 2023-11-18 03:54:58

sologuitar
Member
Registered: 2022-09-19
Posts: 467

### Re: Square Root Raised to Square Root

KerimF wrote:

May I add...

The main difficulty in solving a practical problem is to find the formulas/equations which will lead, usually by using math tricks, to the end values to be applied for a certain project.

We are fortunate now that, for solving an equation or formula, there are many numerical tools (likely PC programs), to choose from, which help us find the numerical answer(s) we are looking for.

For instance, solving a new problem whose formulas/equations are not known yet by humans, even the most intelligent robot cannot do it. Otherwise, humans will be no more needed in research departments

Everything you stated I already know.

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