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.