Sasi Math (Revised for 1024)

Scroll:Real number system >> Decimal places >> ps (4196)

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.

Find the value of the following upto 3 decimal places. Given that √ 2 ≈ 1.414. √ 5 ≈ 2.236. √ 10 ≈ 3.162 √ 3 ≈ 1.732

1	=
√ 10 +√ 5

Answer:_______________

Find the value of the following upto 3 decimal places. Given that √ 3 ≈ 1.732

5-√ 3	=
√ 3

Answer:_______________

Find the value of a and b (use / like $\frac{x}{y)}$

√ 6	=	a+b√ 6
√ 5 -√ 6

a =

b =

Answer:_______________

Find the value of a and b,

√ 5 +1	+	√ 5 -1	a+b√ 5
√ 5 -1		√ 5 +1

a =

b =

Answer:_______________

Find the value of the following upto 3 decimal places. Given that √ 2 ≈ 1.414. √ 5 ≈ 2.236. √ 10 ≈ 3.162

3-√ 5	=
3+2√ 5

Answer:_______________

Find the value of the following upto 3 decimal places. Given that √ 2 ≈ 1.414. √ 5 ≈ 2.236. √ 10 ≈ 3.162

√ 5 +√ 2	=
√ 5 -√ 2

Answer:_______________

Find the value of a and b,

(√ 3 +1)²	=	a+b√ 3
4 -2√ 3

a =

b =

Answer:_______________

Find the value of the following upto 3 decimal places. Given that √ 2 ≈ 1.414. √ 5 ≈ 2.236. √ 10 ≈ 3.162 √ 3 ≈ 1.732

√ 3 +1	=
√ 3 -1

Answer:_______________

Find the value of the following upto 3 decimal places. Given that √ 2 ≈ 1.414. √ 5 ≈ 2.236. √ 10 ≈ 3.162

√ 10 -√ 5	=
√ 2

Answer:_______________

10)

Find the value of the following upto 3 decimal places. Given that √ 2 ≈ 1.414. √ 5 ≈ 2.236. √ 10 ≈ 3.162 √ 3 ≈ 1.732

1	=
√ 10 +√ 5

Answer:_______________

Find the value of the following upto 3 decimal places. Given that √ 2 ≈ 1.414. √ 5 ≈ 2.236. √ 10 ≈ 3.162 √ 3 ≈ 1.732

1	=	Answer: 0.185
√ 10 +√ 5

SOLUTION 1 :

1	=	1	x	√ 10 -√ 5	=	√ 10 -√ 5	=
√ 10 +√ 5		√ 10 + √ 5		√ 10 -√ 5		(√ 10 )² - (√ 5 )²

⇒

√ 10 -√ 5	=	3.162 - 2.236	=
10 - 5		5

⇒

0.1852	=	0.185

Find the value of the following upto 3 decimal places. Given that √ 3 ≈ 1.732

5-√ 3	=	Answer: 1.887
√ 3

SOLUTION 1 :

5-√ 3	=	5-√ 3	x	√ 3	=	5√ 3 -√ 3 .√ 3	=	5√ 3 -3
√ 3	=	√ 3	x	√ 3	=	3	=	3

5(1.732)-3	=	8.660-3	=	5.660	=	1.887
3		3		3

Find the value of a and b (use / like $\frac{x}{y)}$

√ 6	=	a+b√ 6
√ 5 -√ 6

a = Answer: $\frac{31}{19}$

b = Answer: $\frac{10}{19}$

SOLUTION 1 :

5+√ 6	=	5+√ 6	x	5+√ 6	=	(5+√ 6 )²	=
5 -√ 6		5- √ 6		5+√ 6		(5)² - (√ 6 )²

⇒

5² +10√ 6 +(√ 6 )²	=	25 +10√ 6 +6	=
25 -6		19

⇒

31 +10√ 6	=	31	+	10√ 6	=
19		19		19

⇒ a+ b√ 6

a	=	31		b	=		10
		19					19

Find the value of a and b,

√ 5 +1	+	√ 5 -1	a+b√ 5
√ 5 -1		√ 5 +1

a = Answer: 3

b = Answer: 0

SOLUTION 1 :

Given

√ 5 +1	+	√ 5 -1	=	a+b√ 5
√ 5 -1		√ 5 +1

Now

Remainder : (a+b)²= a²+2ab+b²

: (√ 5 +1)² = (√ 5 )² + 2.√ 5 .1+1²

: = 3+2√ 5 +1 = 4+2√ 5

A	=		√ 5 +1	....	B	=	√ 5 -1
			√ 5 -1				√ 5 +1

A=	√ 5 +1	=	√ 5 +1	x	√ 5 +1	=	(√ 5 +1)²	=
	√ 5 -1		√ 5 -1		√ 5 +1		√ 5 )²-(1)²

⇒

(√ 5 )²+2√ 5 .1+1²	=	5+2√ 5 +1	=	6+2√ 5
5-1		4		4

⇒

B=	√ 5 -1	=	√ 5 -1	x	√ 5 -1	=	(√ 5 -1)²	=
	√ 5 +1		√ 5 -1		√ 5 -1		√ 5 )²- (1)²

(√ 5 )^2-2√ 5 .1+1²	=	5-2√ 5 +1	=	6-2√ 5
5-1		4		4

Here, A+B

√ 5 +1	+	√ 5 -1	=	a+b√ 5
√ 5 -1		√ 5 +1

A+B=	6+2√ 5	+	6-2√ 5	=	6 +~~2√ 5~~ + 6 -~~{ s5}~~~~√ 5~~	=	12	=	3
	4		4		4		4

3 = a+b√ 5

3 + 0√ 5 = a+b√ 5

a = 3 b = 0

Find the value of the following upto 3 decimal places. Given that √ 2 ≈ 1.414. √ 5 ≈ 2.236. √ 10 ≈ 3.162

3-√ 5	=	Answer: 0.102
3+2√ 5

SOLUTION 1 :

3-√ 5	=	3-√ 5	x	3-2√ 5	=	(3-√ 5 )x(3-2√ 5	=
3+2√ 5		3+2√ 5		3-2√ 5		3²- (2√ 5 )²

⇒

3.3 - 3.2√ 5 - 3√ 5 +2√ 5 .√ 5	=	9-6√ 5 -3√ 5 +2.5	=
9 - 20		-11

⇒

9 -9√ 5 +10	=	19 -9√ 5	=	- (9√ 5 -19)	=
-11		-11		-11

⇒

20.124 - 19	=	1.124	=	0.102
11		11

Find the value of the following upto 3 decimal places. Given that √ 2 ≈ 1.414. √ 5 ≈ 2.236. √ 10 ≈ 3.162

√ 5 +√ 2	=	Answer: 4.441
√ 5 -√ 2

SOLUTION 1 :

Remainder : (a+b)(a+b) = (a+b)²

(a+b)(a-b) = (a+b)²

√ 5 +√ 2	=	√ 5 +√ 2	x	√ 5 +√ 2	=	(√ 5 +√ 2 )²	=
√ 5 -√ 2		√ 5 - √ 2		√ 5 +√ 2		(√ 5 )² - (√ 2 )²

⇒

(√ 5 )² +2√ 5 .√ 2 +(√ 2 )²	=	5 +2√ 10 +2	=
5 -2		3

⇒

7 +2√ 10	=	7 +2x(3.162)	=	7 +6.324	=
3		3		3

⇒

13.324	=	4.441
3

Find the value of a and b,

(√ 3 +1)²	=	a+b√ 3
4 -2√ 3

a = Answer: 7

b = Answer: 4

SOLUTION 1 :

Given

(√ 3 +1)²	=	a+b√ 3
4 -2√ 3

Now

Remainder : (a+b)²= a²+2ab+b²

: (√ 3 +1)² = (√ 3 )² + 2.√ 3 .1+1²

: = 3+2√ 3 +1 = 4+2√ 3

(√ 3 +1)²	=	4+1√ 3	x	4+2√ 3	=	(4+2√ 3 )²	=
4-2√ 3		4- 2√ 3		4+2√ 3		(4)² - (2√ 3 )²

⇒

4²+2.4.2√ 3 +(2√ 3 )²	=	16+16√ 3 +12	=
16-12		4

⇒

28+16√ 3	=	728	+	416	√ 3	7+4√ 3
4		4		4

⇒ a+ b√ 3

Find the value of the following upto 3 decimal places. Given that √ 2 ≈ 1.414. √ 5 ≈ 2.236. √ 10 ≈ 3.162 √ 3 ≈ 1.732

√ 3 +1	=	Answer: 3.732
√ 3 -1

SOLUTION 1 :

Remainder : (a+b)(a+b) = (a+b)²

(a+b)(a-b) = (a+b)²

√ 3 +1	=	√ 3 +1	x	√ 3 +1	=	(√ 3 +1)²	=
√ 3 -1		√ 3 - 1		√ 3 +1		(√ 3 )² - 1²

⇒

2 (2 +√ 3 )	=	4 +2√ 3	=
2		2

⇒

2 + 1.732	=	3.732

⇒

Find the value of the following upto 3 decimal places. Given that √ 2 ≈ 1.414. √ 5 ≈ 2.236. √ 10 ≈ 3.162

√ 10 -√ 5	=	Answer: 0.655
√ 2

SOLUTION 1 :

√ 10 -√ 5	=	√ 10 -√ 5	x	√ 2	=	√ 10 x√ 2 -√ 5 x√ 2	=	√ 20 -√ 5
√ 2	=	√ 2	x	√ 2	=	2	=	2

√ 4x5-√ 10	=	2√ 5 -√ 10	=
2		2

⇒

2(2.236)-3.162	=	4.472 - 3.162	1.310	=	0.655
2		2	2

10)

Find the value of the following upto 3 decimal places. Given that √ 2 ≈ 1.414. √ 5 ≈ 2.236. √ 10 ≈ 3.162 √ 3 ≈ 1.732

1	=	Answer: 0.185
√ 10 +√ 5

SOLUTION 1 :

1	=	1	x	√ 10 -√ 5	=	√ 10 -√ 5	=
√ 10 +√ 5		√ 10 + √ 5		√ 10 -√ 5		(√ 10 )² - (√ 5 )²

⇒

√ 10 -√ 5	=	3.162 - 2.236	=
10 - 5		5

⇒

0.1852	=	0.185