Vidaara.orgClass 8 · Mathematics
CodeVID-M08-02-SUR-01
Surds - Simplification & Operations - Assignment
Name: ____________________
Roll No.: __________
Date: ____________
General Instructions
- All questions are compulsory.
- Section A carries 1 mark each, Section B 2 marks, Section C 3 marks and Section D 5 marks.
- Show all working for Sections B, C and D. Only final answers are given at the end — for full solutions, raise your doubts with your teacher.
Section A — Multiple Choice Questions
5 × 1 = 5 marks
1.
$\sqrt a\times\sqrt b=$
- A.$\sqrt{a+b}$
- B.$\sqrt{ab}$
- C.$ab$
- D.$\sqrt a+\sqrt b$
2.
$\sqrt8=$
- A.$2\sqrt2$
- B.$4\sqrt2$
- C.$2\sqrt4$
- D.$8$
3.
$\sqrt{\tfrac{9}{16}}=$
- A.$\tfrac34$
- B.$\tfrac49$
- C.$\tfrac{9}{16}$
- D.$\tfrac43$
4.
$\sqrt a\times\sqrt a=$
- A.$a$
- B.$2a$
- C.$a^2$
- D.$\sqrt a$
5.
Rationalising removes the surd from the:
- A.numerator
- B.denominator
- C.whole number
- D.power
Section B — Short Answer (2 marks)
4 × 2 = 8 marks
6.
Simplify $\sqrt{12}$.
7.
Simplify $\sqrt{50}$.
8.
Simplify $\sqrt a\times\sqrt a$.
9.
Rationalise $\tfrac{1}{\sqrt3}$.
Section C — Short Answer (3 marks)
4 × 3 = 12 marks
10.
Simplify $\sqrt{18}+\sqrt2$.
11.
Simplify $\sqrt{75}-\sqrt{12}$.
12.
Multiply $\sqrt6\times\sqrt8$.
13.
Rationalise $\tfrac{5}{\sqrt5}$.
Section D — Long Answer (5 marks)
2 × 5 = 10 marks
14.
Simplify $2\sqrt{27}+\sqrt{48}-\sqrt{12}$.
15.
Rationalise the denominator of $\dfrac{1}{\sqrt5-\sqrt3}$.
Answer Key
Section A — Multiple Choice Questions
- (B) $\sqrt{ab}$
- (A) $2\sqrt2$
- (A) $\tfrac34$
- (A) $a$
- (B) denominator
Section B — Short Answer (2 marks)
- $2\sqrt3$.
- $5\sqrt2$.
- $a$.
- $\tfrac{\sqrt3}{3}$.
Section C — Short Answer (3 marks)
- $4\sqrt2$.
- $3\sqrt3$.
- $4\sqrt3$.
- $\sqrt5$.
Section D — Long Answer (5 marks)
- $8\sqrt3$.
- $\dfrac{\sqrt5+\sqrt3}{2}$.
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