Solve Arithmetic Expression \(9^2 + \sqrt{8^2} - 10\sqrt{49} - 20\)
This solution details the step-by-step calculation for the given arithmetic expression, evaluating exponents and square roots to find the final value.
Evaluating the Expression
The expression to evaluate is:
\(9^2 + \sqrt{8^2} - 10\sqrt{49} - 20\)
Calculation Steps
Follow these steps to simplify the expression:
- Step 1: Evaluate the exponents.
Calculate \(9^2\).
\(9^2 = 81\)
- Step 2: Evaluate the square roots.
Calculate \(\sqrt{8^2}\) and \(\sqrt{49}\).
\(\sqrt{8^2} = \sqrt{64} = 8\)
\(\sqrt{49} = 7\)
- Step 3: Substitute the values back into the expression.
The expression becomes:
\(81 + 8 - 10(7) - 20\)
- Step 4: Perform multiplication.
Calculate \(10 \times 7\).
\(10 \times 7 = 70\)
The expression is now:
\(81 + 8 - 70 - 20\)
- Step 5: Perform addition and subtraction from left to right.
First, add \(81 + 8\).
\(81 + 8 = 89\)
The expression is now:
\(89 - 70 - 20\)
Next, subtract \(89 - 70\).
\(89 - 70 = 19\)
The expression is now:
\(19 - 20\)
Finally, subtract \(19 - 20\).
\(19 - 20 = -1\)
Final Result
The value of the expression \(9^2 + \sqrt{8^2} - 10\sqrt{49} - 20\) is -1.
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