You cannot change 7.5 into a square root because it a decimal & is not one of the root-able numbers, you can get a result with a calculator,
but there is a formula that can produce a very, very, close result. The error can vary from 0.000 to 0.00000000 so it produces a very exact result, so you may want to write the formula down...
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The formula is:
√x ≈ ___x+r____ (r= closest root to x)
2·√r (x= the number you wanna root,
in your case: 7.5)
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Let's start
___7.5+9____
2·3
The formula is ready:
7.5 is x, the number you wanna find out,
9 is the closest real root to 7.5 (nine's root is 3).
3 is equal to √r (r is 9).
And finally 2, (2 is already part of the formula).
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___7.5+9____ (7.5 + 9= 16.5)
2 · 3 (2 · 3= 6)
So far, so good right? ;)
___16.5____ (Now with a long division on paper, I see
6 16.5 ÷ 6= 2.75)
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Now we have the Answer!
The answer is 2.75!
Well that's approximation of √7.5!
Now Let's see the √7.5 on a calculator to see how exact my formula is.
On a calculator the √7.5= 2.738612788... and on my formula the answer is 2.75! Pretty exact huh?
It's good for you to keep that formula with you whenever you need it!
Good Luck on your studies!
David Edward. :)