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
If P = 0.3 × 0.3 + 0.03 × 0.03 - 0.6 × 0.03 and Q = 0.54, then \(\rm \frac{P}{Q}\) is equal to:
The value of \(\left(\frac{1}{2}\right)^{−2} \times\left(\frac{1}{3}\right)^{−2} \times\left(\frac{1}{4}\right)^{−2} \) is
The solution of the equation \(\frac{2}{3 x-4}+\frac{2}{2 x-6}=0 \) is:
If \(\rm \sqrt{1225 \times \sqrt{32 \div x}}= 70\) find the value of x.
What will come in the place of question mark (?) in the given expression?
\(\sqrt{21+\sqrt{49}+\sqrt{64}} \space {\%\:of\:5000}=?\)
