Use the formula $F = \frac{s}{\sqrt{tm}}$ to find the value of $F$ when $s = 5.8 \times 10^6$ t = $4.1 \times 10^8$ $m = 3.7 \times 10^{-2}$ Give your answer in standard form, correct to 2 significant figures. - OCR - GCSE Maths - Question 2 - 2019 - Paper 4

Next, we find the square root of $tm$:

$\sqrt{tm} = \sqrt{1.537 \times 10^7}$

Using the properties of square roots gives:

$\sqrt{tm} = \sqrt{1.537} \times \sqrt{10^7}$ $\sqrt{1.537} \approx 1.24$ $\sqrt{10^7} = 10^{3.5} = 3.162 \times 10^3$

Thus:

$\sqrt{tm} \approx 1.24 \times 3.162 \times 10^4 \approx 3.91 \times 10^4$

Now, substitute the values of $s$ and $\sqrt{tm}$ into the formula for $F$:

$F = \frac{s}{\sqrt{tm}} = \frac{5.8 \times 10^6}{3.91 \times 10^4}$

Calculating the fraction gives:

$F \approx 1.48 \times 10^2$

Finally, we express this answer in standard form, correct to 2 significant figures:

$F = 1.5 \times 10^2$