# Need help converting decimal into radical simplest form

#### Shogun

##### New member
I got the answer to a problem in decimal form and I have to convert it into a radical in simplest form. Can someone please show me how to convert 86.6026404 into radical simplest form?

#### stapel

##### Super Moderator
Staff member
Without knowing the process that generated this decimal approximation, the best one could do would be to guess a radical approximation.

Please reply with the full and exact text of the exercise, the complete instructions, and a clear listing of how you arrived at this value. Thank you.

Eliz.

#### Gene

##### Senior Member
That is VERY close to sqrt(7500). (Yes, that is a guess.)
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Gene

#### Denis

##### Senior Member
Shogun said:
I got the answer to a problem in decimal form and I have to convert it into a radical in simplest form. Can someone please show me how to convert 86.6026404 into radical simplest form?
Should that be 86.6025404, Shogun?

if so, then sqrt(7500) or 50sqrt(3) ; as per Gene.

#### Shogun

##### New member
The whole problem or question was: Use what you know about 30-60-90 triangles to find the value of h in the rhombus. Then use the value to find the area of the rhombus. Express your answers as radicals in simplest form.

This is how I solved

S = O/H

Sin 60 degrees = 0.866025404

H = 8. 66026404

A = B X H 8.66026404 X 10 = 86.6026404

Here is where I get stuck.

#### soroban

##### Elite Member
Hello, Shogun!

The whole problem or question was: Use what you know about 30-60-90 triangles to find the value of h in the rhombus. Then use the value to find the area of the rhombus. Express your answers as radicals in simplest form.

This is how I solved

S = O/H

Sin 60 degrees = 0.866025404 $$\displaystyle \;\;$$ ← here!
You used your calculator, didn't you?
$$\displaystyle \;\;$$No wonder you have no radicals in your answer!

You're expected know that: $$\displaystyle \,\sin 60^o\,=\,\frac{\sqrt{3}}{2}$$

#### Shogun

##### New member
Yea, I actually did use my calculator. I can be frustrating when you are a distance learner and the book you are given doesn't explain things thoroughly. I am not exactly sure what to do next. Do I now multiply that by 10?

#### stapel

##### Super Moderator
Staff member
Shogun said:
Do I now multiply that by 10?
Do you multiply what by 10?

And where is "10" coming from? You don't list it in "the whole problem" you quoted.

Thank you.

Eliz.