Calculate $\frac{-11 + \sqrt{(-11)^2 - \dfrac{20}{11}}}{8 \times 0.6}.$ Write your answer correct to 4 significant figures. Write your answer to part (a) in standard form.

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Worked solution

1. Evaluate the expression using the correct order of operations

\frac{-11 + \sqrt{(-11)^2 - \dfrac{20}{11}}}{8 \times 0.6} = \frac{-11 + \sqrt{121 - \dfrac{20}{11}}}{4.8}

= \frac{-11 + \sqrt{119.1818\ldots}}{4.8} = \frac{-11 + 10.9161\ldots}{4.8}

$= -0.017476\ldots$

2. Round the calculator value to 4 significant figures

$-0.017476\ldots \approx -0.01748 \quad \text{to 4 significant figures}$

Answer

$-0.03780$

1. Convert the answer from part (a) into standard form

From part (a), the answer is $-0.03780$ .

$-0.03780=-3.780\times 10^{-2}$

Answer

$-3.780 \times 10^{-2}$

AI analysis — may contain mistakes.

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