Question 1: Simplify: √48 + √12

Answer: 4√3

Question 2: Calculate: 5√7 - 2√7

Answer: 3√7

Question 3: Express as a single surd: √75 + 2√75

Answer: 3√75

Question 4: Simplify: 3√18 - √50

Answer: 3×3√2 - 5√2 = 9√2 - 5√2 = 4√2

Question 5: If √x + √x = 10, find the value of √x.

Answer: √x = 5

Question 6: Solve for √x: 4√x - 3√x = 2

Answer: √x = 2

Question 7: A box contains √20 and √5. If you add √20 and √5, what is the simplified form?

Answer: 2√5 + √5 = 3√5

Question 8: A student simplifies √80 - √12 as 4√5 - 2√3. Is this correct? Explain.

Answer: No, because √80 = 4√5 (correct), but √12 = 2√3 (correct), so the result is 4√5 - 2√3, which is correct. The student is correct.

Question 9: Construct an expression with two like surds that sums to 7√2.

Answer: 4√2 + 3√2

Question 10: Identify and correct the mistake: Simplify √27 + √3 as 2√3.

Answer: √27 = 3√3, so √27 + √3 = 3√3 + √3 = 4√3, not 2√3. The mistake is incorrectly simplifying √27 as 2√3.

Question 11: Prove that √50 + √2 can be expressed in terms of √2.

Answer: √50 = 5√2, so √50 + √2 = 5√2 + √2 = 6√2.

Question 12: Plot the graph of y = 2√x for x from 0 to 9 on the grid.

Answer: Student plots points at (0,0), (1, 2), (4, 4), (9, 6).