The value of $\sqrt{ \left(42 + \sqrt{ \left(46 + \sqrt{ \left(3 +\sqrt{ \left(34+ \sqrt{(4)}\right)} \right) }\right)}\right)}$ is:
Nested Square Roots Evaluation
This problem requires simplifying a mathematical expression with multiple nested square roots. We solve it step-by-step, starting from the innermost root and working outwards.
Radical Expression Step-by-Step Solution
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Evaluate the innermost square root: $\sqrt{(4)}$.
Calculation: $ \sqrt{(4)} = 2 $
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Substitute this result into the expression $34 + \sqrt{(4)}$.
Calculation: $34 + 2 = 36$.
Evaluate the square root: $ \sqrt{36} = 6 $
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Substitute this result into the expression $3 + \sqrt{(34+ \sqrt{(4)})}$.
Calculation: $3 + 6 = 9$.
Evaluate the square root: $ \sqrt{9} = 3 $
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Substitute this result into the expression $46 + \sqrt{(3 + \sqrt{(34+ \sqrt{(4)})})}$.
Calculation: $46 + 3 = 49$.
Evaluate the square root: $ \sqrt{49} = 7 $
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Substitute this result into the final expression $42 + \sqrt{(46 + \sqrt{(3 + \sqrt{(34+ \sqrt{(4)})})})}$.
Calculation: $42 + 7 = 49$.
Evaluate the final square root: $ \sqrt{49} = 7 $
Final Value Determination
The step-by-step simplification confirms that the value of the given nested square root expression is 7.
Important Questions from Simplification
The value of {5 - 5 ÷ (10 - 12) × 8 + 9} × 3 + 5 + 5 × 5 ÷ 5 of 5 is:
What should come in place of the question mark (?) in the following question?
[((16 ÷ 4) × 4) ÷ 4] = ?
Simplify the following expression.
\(\frac{{6\frac{1}{2} + 2\frac{5}{7} \times \frac{{14}}{{19}} - \frac{1}{2} \div 2\ of\frac{1}{4}}}{{11 \times 12 \div 12 + 12}}\)
The value of \(\left( {\frac{7}{5} \div \frac{7}{{10}}of\frac{3}{4}} \right) \div \frac{4}{9} + \left( {\frac{7}{{16}} \div 10\frac{1}{2} \times 7\frac{1}{5}} \right) \times \frac{5}{{12}} \) is:
The value of \(\left( {{1 \over 2}} \right)\) [{–2(12 + 2)}10] is:
