Question 1: Simplify the expression \( \frac{3}{\sqrt{2}} \).

Answer: 3\sqrt{2}/2

Question 2: Rationalise the denominator of \( \frac{5}{\sqrt{5}} \).

Answer: 5

Question 3: Express \( \frac{7}{\sqrt{3}} \) in simplified form.

Answer: 7\sqrt{3}/3

Question 1: Explain the steps to rationalise the denominator of \( \frac{4}{\sqrt{6}} \).

Answer: Multiply numerator and denominator by \( \sqrt{6} \), then simplify.

Question 2: If \( \frac{a}{\sqrt{b}} \) is simplified correctly, what should the numerator and denominator become after rationalising? Provide a general explanation.

Answer: Numerator: \( a \) multiplied by \( \sqrt{b} \); Denominator: \( b \)

Question 1: A surveyor measures a distance of \( \frac{20}{\sqrt{5}} \) meters along a diagonal. Express this distance in simplified form for easier interpretation.

Answer: 20\sqrt{5}/5=4\sqrt{5}

Question 1: Simplify \( \frac{6\sqrt{3}}{\sqrt{12}} \).

Answer: 6\sqrt{3} \times \frac{\sqrt{12}}{\sqrt{12}}=6\sqrt{3} \times \frac{\sqrt{12}}{\sqrt{12}}=6\sqrt{3} \times \frac{2\sqrt{3}}{\sqrt{12}}=6\sqrt{3} \times \frac{2\sqrt{3}}{2\sqrt{3}}=6\sqrt{3} \times \frac{\sqrt{3}}{\sqrt{3}}=6\times 3=18

Question 2: Construct an expression in the form \( \frac{a}{\sqrt{b}} \) and rationalise it correctly, explaining the process.

Answer: Example: \( \frac{9}{\sqrt{2}} \). Multiply numerator and denominator by \( \sqrt{2} \) to get \( \frac{9\sqrt{2}}{2} \).

Question 1: A student simplifies \( \frac{8}{\sqrt{2}} \) incorrectly as \( \frac{8}{\sqrt{2}}=\frac{8\sqrt{2}}{2} \). Is this correct? If not, what mistake is made and what is the correct simplification?

Answer: No, the mistake is in multiplying numerator and denominator by \( \sqrt{2} \) instead of rationalising properly. Correct form: \( 8\sqrt{2}/2=4\sqrt{2} \).

Question 2: Identify the error in simplifying \( \frac{5}{\sqrt{3}} \) as \( \frac{5\sqrt{3}}{\sqrt{3}} \) and correct it.

Answer: The mistake is canceling \( \sqrt{3} \) directly; the proper method is to multiply numerator and denominator by \( \sqrt{3} \), resulting in \( 5\sqrt{3}/3 \).