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Evaluate: (8.6)^(2)-(1.4)^(2)...

Evaluate:
`(8.6)^(2)-(1.4)^(2)`

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The correct Answer is:
To evaluate the expression \( (8.6)^2 - (1.4)^2 \), we can use the algebraic identity for the difference of squares, which states: \[ A^2 - B^2 = (A + B)(A - B) \] ### Step-by-step Solution: 1. **Identify A and B**: - Let \( A = 8.6 \) - Let \( B = 1.4 \) 2. **Apply the difference of squares formula**: - According to the formula, we can rewrite the expression: \[ (8.6)^2 - (1.4)^2 = (8.6 + 1.4)(8.6 - 1.4) \] 3. **Calculate \( A + B \)**: - Calculate \( 8.6 + 1.4 \): \[ 8.6 + 1.4 = 10.0 \] 4. **Calculate \( A - B \)**: - Calculate \( 8.6 - 1.4 \): \[ 8.6 - 1.4 = 7.2 \] 5. **Multiply the results**: - Now substitute back into the expression: \[ (8.6)^2 - (1.4)^2 = (10.0)(7.2) \] - Calculate \( 10.0 \times 7.2 \): \[ 10.0 \times 7.2 = 72.0 \] 6. **Final Result**: - Therefore, the evaluated result of \( (8.6)^2 - (1.4)^2 \) is: \[ \boxed{72} \]
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Knowledge Check

  • Find the value of (8^(4)+8^(2))^((1)/(2))

    A
    84
    B
    `8 sqrt(77)`
    C
    72
    D
    `8 sqrt(65)`
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    D
    `8sqrt(65)`
  • Find the value of v : 10 (1)/(2) - [8(1)/(2) + { 7 - bar(6-4)}] bar(6-4) =2 (v)

    A
    -3
    B
    -2
    C
    1
    D
    4
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