Question
Calculate
\(\sqrt{\frac{1}{0.01}-8^{2}}\)
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▶️Answer/Explanation
To calculate \(\sqrt{\frac{1}{0.01}-8^{2}}\), we can follow these steps:
Simplify the expression inside the square root.
\(\frac{1}{0.01}-8^{2}\)
\(= \frac{1}{0.01} – 64\)
\(= 100 – 64\)
\(= 36\)
Take the square root of the simplified expression.
\(\sqrt{36} = 6\)
Therefore, \(\sqrt{\frac{1}{0.01}-8^{2}}\) equals 6.
Question
\(\pi\) \( 3^{-2}\) \( 3\frac{4}{7}\) 33.3% \(\sqrt{3}\) \(0.3 3^{999}\)
From this list, write down the two numbers that are irrational.
…………………. , ………………..
▶️Answer/Explanation
The two numbers that are irrational from the given list are:
\(\pi\) (pi) – Pi is an irrational number, which means it cannot be expressed as a finite fraction or a terminating or repeating decimal.
\(\sqrt{3}\) (square root of 3) – The square root of 3 is also an irrational number, as it cannot be expressed as a fraction or a terminating or repeating decimal.
Therefore, the two irrational numbers from the given list are \(\pi\) and \(\sqrt{3}\).
Question
Without using a calculator, estimate, by rounding each number correct to 1 significant figure,
\(\frac{\sqrt{104.3}}{8.72-7.389}\)
You must show all your working.
▶️Answer/Explanation
To estimate the expression \(\frac{\sqrt{104.3}}{8.72-7.389}\) with rounded numbers:
Round each number to 1 significant figure.
\(\sqrt{104.3} \approx 10\)
\(8.72 – 7.389 \approx 9-7\)
Substitute the rounded values into the expression.
\(\frac{\sqrt{104.3}}{8.72-7.389} \approx \frac{10}{2}\)
Simplify the expression.
\(\frac{10}{2} \approx 5\)
Therefore, the estimated value of the expression \(\frac{\sqrt{104.3}}{8.72-7.389}\) rounded to 1 significant figure is approximately 5.