Find the length of one side of a square garden in metres, given its area in Hectometres squared.

The area ($A$) of a square is given by the square of its side length ($s$).

$$A = s^2$$

Therefore, the side length is the square root of the area.

$$s = \sqrt{A}$$

We know that $1 \text{ Hm} = 100 \text{ m}$.
So, $1 \text{ Hm}^2 = (100 \text{ m})^2 = 10000 \text{ m}^2$.
Given area $A = 17.64 \text{ Hm}^2$.

$$A = 17.64 \times 10000 \text{ m}^2$$ $$A = 176400 \text{ m}^2$$

$$s = \sqrt{176400 \text{ m}^2}$$ $$s = \sqrt{1764 \times 100} \text{ m}$$ $$s = \sqrt{1764} \times \sqrt{100} \text{ m}$$ $$s = 42 \times 10 \text{ m}$$ $$s = 420 \text{ m}$$

The length of one side of the square garden is:

$$\boxed{420 \text{ m}}$$

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The question asks to write numbers in standard form, but no numbers are provided in the image for this question. Please provide the numbers you would like to convert to standard form.

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The question asks for the original number of learners given an increase ratio and the new number of students.

The number of students increased in the ratio $8:7$. This means the new number of students is to the original number of students as 8 is to 7.
Let $N_{original}$ be the original number of learners.
Let $N_{new}$ be the new number of learners.

$$\frac{N_{new}}{N_{original}} = \frac{8}{7}$$

The number of students after the increase was 560. So, $N_{new} = 560$.

$$\frac{560}{N_{original}} = \frac{8}{7}$$

Multiply both sides by $7 \times N_{original}$ to clear the denominators.

$$560 \times 7 = 8 \times N_{original}$$

Divide by 8:

$$N_{original} = \frac{560 \times 7}{8}$$ $$N_{original} = 70 \times 7$$ $$N_{original} = 490$$

The original number of learners was:

$$\boxed{490}$$