In psychology, it has been suggested that the number $$ S $$ of nonsense syllables that a person can repeat consecutively depends on his or her IQ score I according to the equation $$ S=2 \sqrt{1}-9 $$. Use this relationship to estimate the IQ of a person who can repeat 7 nonsense syllables consecutively. $$ I=\square $$ (Round to the nearest integer as needed.)

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To estimate the IQ of a person who can repeat 7 nonsense syllables consecutively, we can use the given relationship between the number of nonsense syllables $$ S $$ and the IQ score $$ I $$ as follows:

Given equation: $$ S = 2 \sqrt{I} - 9 $$

We are given that $$ S = 7 $$, so we can substitute this value into the equation to solve for $$ I $$:

$$ 7 = 2 \sqrt{I} - 9 $$

Now, we can solve for $$ I $$ by isolating it on one side of the equation.
Solve the equation by following steps:
- step0: Solve for $$I$$:
  $$7=2\sqrt{I}-9$$
- step1: Find the domain:
  $$7=2\sqrt{I}-9,I\geq 0$$
- step2: Swap the sides:
  $$2\sqrt{I}-9=7$$
- step3: Move the constant to the right side:
  $$2\sqrt{I}=7-\left(-9\right)$$
- step4: Calculate:
  $$2\sqrt{I}=16$$
- step5: Divide both sides:
  $$\sqrt{I}=8$$
- step6: Raise both sides to the $$2$$-th power$$:$$
  $$\left(\sqrt{I}\right)^{2}=8^{2}$$
- step7: Evaluate the power:
  $$I=64$$
- step8: Check if the solution is in the defined range:
  $$I=64,I\geq 0$$
- step9: Find the intersection:
  $$I=64$$
- step10: Check the solution:
  $$I=64$$
The solution to the equation is $$ I = 64 $$.

Therefore, the estimated IQ of a person who can repeat 7 nonsense syllables consecutively is 64.
The estimated IQ is 64.

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