Evaluating Nested Square Root Expression
The problem requires simplifying the following nested radical expression:
$ \sqrt{93 + \sqrt{32 + \sqrt{274 + \sqrt{225}}}} $
We simplify this expression by working from the inside out.
Innermost Calculation
First, calculate the square root of the innermost number:
$ \sqrt{225} = 15 $
Second Layer Calculation
Substitute this result back into the expression:
$ \sqrt{274 + 15} $
Now, calculate this new square root:
$ \sqrt{289} = 17 $
Third Layer Calculation
Substitute this result back:
$ \sqrt{32 + 17} $
Calculate the square root:
$ \sqrt{49} = 7 $
Outermost Layer Calculation
Finally, substitute this result into the outermost part:
$ \sqrt{93 + 7} $
Calculate the final square root:
$ \sqrt{100} = 10 $
Final Result
The evaluated value of the expression $ \sqrt{93 + \sqrt{32 + \sqrt{274 + \sqrt{225}}}} $ is 10.
Similar Questions
If (584)2 = 341056, then the value of square root of 34.1056 is:
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- The least number to be added to 435 to make it a perfect square is?
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Important Questions from Square and Square Root
The addition of the squares of two numbers in squares is 221. What are those numbers?
Find the value of \(\sqrt{9604} \).
If (584)2 = 341056, then the value of square root of 34.1056 is:
Which one of the following numbers is not a square of any natural number?
The value of \(\sqrt{72+\sqrt{72 +\sqrt{72+.....\infty}}}\) is :
