To find the value of the given nested radical expression, we simplify it step-by-step, starting from the innermost part.
Simplifying the Nested Radical Expression
Step 1: Evaluate the Innermost Radical
The innermost part of the expression is $\sqrt{16}$.
Calculation:
$ \sqrt{16} = 4 $
Step 2: Evaluate the Next Nested Radical
Substitute the result from Step 1 into the next radical:
Expression becomes $\sqrt{12 + 4}$.
Calculation:
$ \sqrt{12 + 4} = \sqrt{16} = 4 $
Step 3: Evaluate the Third Nested Radical
Substitute the result from Step 2 into the next radical:
Expression becomes $\sqrt{221 + 4}$.
Calculation:
$ \sqrt{221 + 4} = \sqrt{225} $
We know that $15^2 = 225$, so:
$ \sqrt{225} = 15 $
Step 4: Evaluate the Outermost Radical
Substitute the result from Step 3 into the final radical:
Expression becomes $\sqrt{10 + 15}$.
Calculation:
$ \sqrt{10 + 15} = \sqrt{25} $
We know that $5^2 = 25$, so:
$ \sqrt{25} = 5 $
Final Value
The value of the expression $\sqrt{10 + \sqrt{221 + \sqrt{12 + \sqrt{16}}}}$ is 5.
Similar Questions
What will the value of the following expression be?
$\left(\frac{6+3}{3}\right) - 5 \times (4+5)$
- What is the value of the following expression?
$\frac{\sqrt{225}}{14} \times \frac{\sqrt{196}}{22} \times \frac{\sqrt{484}}{15}$ - The value of $\frac{(5.4)^3 - 0.064}{(5.4)^2 + 2.16 + 0.16}$ is:
- Solve the following.
$(1 + \frac{1}{x})(1 + \frac{1}{x+1})(1 + \frac{1}{x+2})(1 + \frac{1}{x+3}) = ?$ - The value of $\sqrt{0.04} + \sqrt{1.44} + \sqrt{1.69} + \sqrt{0.0009}$ is:
- The value of $\sqrt{196} + \sqrt{0.0361} - \sqrt{7.29}$ is ____.
- The value of $\frac{32 \div 4 - 5 \times 8 \div 3}{5 \times 3 - \{6 + 3\}}$ is:
- What is the value of $x$, if $-3 \times \sqrt{196} + \sqrt{x} = 8 \times 3 - 2$?
- What is the value of $\sqrt{\frac{1.21 \times 0.9}{1.1 \times 0.11}}$?
- The value of $\frac{\{(13)^3 - 4^3\}}{13 - 8 \div 2} \div 8 - \{2 + 6 \times 9\}$ is:
Important Questions from Simplification
What will come in the place of the question mark ‘?’ in the following question?
(15 + 24) × 3 ÷ 13 + 18 – 5 = ?
What should come in place of the question mark '?' in the following question?
\n13 × 3 of 5 ÷ 26 = ? + 2.5What should come in place of the question mark '?' in the following question?
10% of 450 - (8 × 5) = ? × 5
What will come in the place of the question mark ‘?’ in the following question?
(66)2 - (34)2 + ?2 = (60)2
What will come in the place of the question mark ‘?’ in the following question?
3 × ? ÷ 9 = ∛729 × √121
