# Finding the Alternate Form of a Square Root: A Mathematical Challenge

• Rat3dR
In summary, the conversation discusses finding an alternate form for the expression sqrt(3+sqrt(8)) and reaching the answer 1+sqrt(2). One suggestion is to try squaring both expressions, and another suggests factoring the expression. The person asking for help was able to find the solution with the assistance of others.
Rat3dR
Hey there,

Square roots never have been my strongest point in maths, but I'm not seeing the trick in this example:

I'm trying to find an alternate form of:
sqrt(3+sqrt(8))
I get as far as:
sqrt(3+2 sqrt(2))

But i know i want to/should end up with:
1+sqrt(2)

I just don't know how to get there... :(

Any help?

Thanks

Try squaring both expressions. Then they become equal, no?

Maybe i should explain my question a little further..

In my calculations I end up with the first (or second) expression (namely sqrt(3+sqrt(8))).. Which is fine, since it's the right answer, however, for convenience I tried to find an alternate, simpler expression, which should be 1+sqrt(2). I found it using Mathematica, but I have NO idea how I'd go from the first expression to the last one.. What are the intermediate steps?

EDIT: I played around a bit, using your useful input, and i think I'm getting the hang of it.. Any advice on how to tackle these kind of simplifications in general would still be great though :)

Last edited:
Rat3dR said:
I'm trying to find an alternate form of:
sqrt(3+sqrt(8))
I get as far as:
sqrt(3+2 sqrt(2))

But i know i want to/should end up with:
1+sqrt(2)

Try sqrt(3+sqrt(8)) --> sqrt(3+2 sqrt(2)) --> sqrt(1+2+2 sqrt(2)) --> (factorise)--> sqrt( (1+sqrt(2))(1+sqrt(2)) ) --> 1+sqrt(2)

Yes, thank you all for your help :). I just needed this little bump to get things going. :)

## 1. What is an alternate form of square root?

An alternate form of square root is a mathematical representation of a square root that does not use the radical symbol ( √ ) and instead uses exponents.

## 2. How do you write an alternate form of square root?

To write an alternate form of square root, you first convert the radical expression into an exponential expression by raising the radicand (the number under the radical symbol) to the power of 1/2.

## 3. Why would you use an alternate form of square root?

An alternate form of square root is often used in mathematical equations to simplify expressions and make them easier to solve.

## 4. What is the difference between the alternate form of square root and the radical form?

The alternate form of square root and the radical form are essentially the same, but the alternate form uses exponents instead of the radical symbol. This can make it easier to manipulate and solve equations.

## 5. Can you convert any square root into an alternate form?

Yes, any square root can be converted into an alternate form. However, it may not always be necessary or beneficial to do so, depending on the specific equation and problem being solved.

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