Written Instructions:
For each Multiple Choice Question (MCQ), four options are given. One of them is the correct answer. Make your choice (1,2,3 or 4). Write your answers in the brackets provided..
For each Short Answer Question(SAQ) and Long Answer Question(LAQ), write your answers in the blanks provided.
Leave your answers in the simplest form or correct to two decimal places.
| 1) Identify which of the following are surds and which are not with reasons. 3√ 4 x 3√ 16
Answer:_______________ |
| 2) Identify which of the following are surds and which are not with reasons. √ 180 x √ 5
Answer:_______________ |
| 3) Simplify 7 3√ 2 + 6 3√ 16 - 3√ 54 3√ 2 Answer:_______________ |
| 4) Simplify ( √ 34 - √ 3 )( √ 34 + √ 3 )
Answer:_______________ |
| 5) Simplify 4 √ 72 - √ 50 - 7 √ 128 √ 2 Answer:_______________ |
| 6) Identify which of the following are surds and which are not with reasons. √ 90 √ Answer:_______________ |
| 7) Simplify (10 + √ 3 )(2 + √ 5 ) 20 + 10√ 5 + 2√ 3 + √ Answer:_______________ |
| 8) Simplify 2 3√ 40 + 33√ 625 - 4 3√ 320 3√ 5 Answer:_______________ |
| 9) Identify which of the following are surds and which are not with reasons. √ 8 x √ 6 √ Answer:_______________ |
| 10) Simplify ( √ 5 + √ 3 )2 2(4 +√ ) Answer:_______________ |
| 1) Identify which of the following are surds and which are not with reasons. 3√ 4 x 3√ 16 Answer: 4 SOLUTION 1 : 3√ 4 x 3√ 16 = 3√ 4x16 = 3√ 4x4x4 = 4 ⇒ 4 is not a surd. |
| 2) Identify which of the following are surds and which are not with reasons. √ 180 x √ 5 Answer: 30 SOLUTION 1 : √ 180 x √ 5 = √ 36x5 x√ 5 = 6√ 5 x √ 5 = 6 x 5 = 30 ⇒ 30 is not a surd. |
| 3) Simplify 7 3√ 2 + 6 3√ 16 - 3√ 54 Answer: 163√ 2 SOLUTION 1 : 7 3√ 2 + 6 3√ 16 - 3√ 54 = 7 3√ 2 + 6 3√ 2x2x2x2 - 3√ 2x3x3x3 = 7 3√ 2 + 12 3√ 2 - 3 3√ 2 = (7 + 12 + - 3) 3√ 2 = 16 3√ 2 |
| 4) Simplify ( √ 34 - √ 3 )( √ 34 + √ 3 ) Answer: 31 SOLUTION 1 : ( √ 34 - √ 3 )( √ 34 + √ 3 ) a = √ 34 , b = √ 3 Hind : (a +b)(a -b) = a2 -b2) (√ 34 + √ 3 )(√ 34 -√ 3 ) = (√ 34 )2 - (√ 3 )2 = 34 - 3 = 31 |
| 5) Simplify 4 √ 72 - √ 50 - 7 √ 128 Answer: -37√ 2 SOLUTION 1 : 4 √ 72 - √ 50 - 7√ 128 4 √ 72 = 4 √ 36x2 = 4x6√ 2 = 24√ 2 √ 50 = √ 25x2 = 5√ 2 7√ 128 = √ 64x2 = 7 x 8√ 2 = 56√ 2 4 √ 72 - √ 50 - 7√ 128 = 24√ 2 - 5√ 2 - 56√ 2 = (24 - 5 - 56)√ 2 = (-37)√ 2 |
| 6) Identify which of the following are surds and which are not with reasons. √ 90 Answer: 3√ Answer: 10 SOLUTION 1 : √ 90 x √ 6 = √ 10x9 = 3√ 10 Since 10 cannot be expressed as a square of any rational number. ⇒ 3√ 10 is a surd. |
| 7) Simplify (10 + √ 3 )(2 + √ 5 ) 20 + 10√ 5 + 2√ 3 + √ Answer: 15 SOLUTION 1 : (10+√ 3 )(2+ √ 5 ) = 20 + 10√ 5 + 2√ 3 + √ 3 x √ 5 = 20 + 10√ 5 + 2√ 3 + √ 15
|
| 8) Simplify 2 3√ 40 + 33√ 625 - 4 3√ 320 Answer: 33√ 5 SOLUTION 1 : 2 3√ 40 + 3 3√ 625 - 4 3√ 320 2 3√ 40 = 2 3√ 2 x 2 x 2 x 5 = 2 x 2 3√ 5 = 4 3√ 5 3 3√ 625 = 3 3√ 5 x 5 x 5 x 5 = 3 x5 3√ 5 = 15 3√ 5 4 3√ 320 = 4 3√ 26 x 5 = 4 x 43 3√ 5 = 16 3√ 5 2 3√ 40 - 3√ 625 - 43√ 320 = 4 3√ 5 + 153√ 5 - 163√ 5 = ( 4 + 15 - 16)3√ 5 = 3 3√ 5 |
| 9) Identify which of the following are surds and which are not with reasons. √ 8 x √ 6 Answer: 4√ Answer: 3 SOLUTION 1 : √ 8 x √ 6 = √ 48 = √ 16x3 = 4√ 3 4 is rational number and √ 3 is an irrational number. ⇒ 4√ 3 is a surd. |
| 10) Simplify ( √ 5 + √ 3 )2 2(4 +√ Answer: 15) SOLUTION 1 : (√ 5 + √ 3 )2 a = √ 5 , b = √ 3 Hind ; (a + b)2 = a2 + 2ab +b2) (√ 5 + √ 3 )2 = (√ 5 )2 + 2√ 3 x √ 5 + (√ 3 )2 = 5 + 2√ 15 + 3 = 8 + 2√ 15 = 2(4 +√ 15 ) |