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:
- The least number to be added to 435 to make it a perfect square is?
- What is the square root of 6561?
- What is the square root of 576?
- The least number that must be subtracted from 7577 to get a perfect square is:
- Square root of 0.9 is equal to
Important Questions from Square and Square Root
The sum of the squares of two positive integers is 306. If the square of the larger integer is 25 times the smaller integer, then the difference between the two integers is
- \(\sqrt{625.0025 }=\)
The least number which is a perfect square and is divisible by each of the numbers 4, 10 and 12 is :
The addition of the squares of two numbers in squares is 221. What are those numbers?
Find the value of \(\sqrt{9604} \).
