221. If		nr − t n +	1		be a perfect square, then the values of t are:
     			4

1. 1. ± 2

   
   
   

   2. 1, 2

   
   
   

   3. 2,3

   
   
   

   4. ± 1

   
   
   

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1. View Hint View Answer Discuss in Forum

   For   nr − t n +	1	to be a perfect square,
   	4

   
   r = 2 and t = ±1
   

   	= n2 − n +	1	= n2 − 2.n	1	+	1	=		n −	1		2
   		4		2		4				2

   
   

   = n2 + n +	1	= n2 + 2.n.	1	+	1	=		n +	1		2
   	4		2		4				2

   Correct Option: D

   For   nr − t n +	1	to be a perfect square,
   	4

   
   r = 2 and t = ±1
   

   	= n2 − n +	1	= n2 − 2.n	1	+	1	=		n −	1		2
   		4		2		4				2

   
   

   = n2 + n +	1	= n2 + 2.n.	1	+	1	=		n +	1		2
   	4		2		4				2

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222. Number of digits in the square root of 62478078 is:

1. 1. 4

   
   
   

   2. 5

   
   
   

   3. 6

   
   
   

   4. 3

   
   
   

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1. View Hint View Answer Discuss in Forum

   Number of digits in 62478078 = 8
   ∴  Number of digits in its square root = 4
   ⇒  √62478078 ≈ 7904
   ⇒  √62473216 = 7904

   Correct Option: A

   Number of digits in 62478078 = 8
   ∴  Number of digits in its square root = 4
   ⇒  √62478078 ≈ 7904
   ⇒  √62473216 = 7904

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223. The simplified value of	√32 + √48	is
     	√8 + √12

1. 1. 3

   
   
   

   2. 2

   
   
   

   3. 6

   
   
   

   4. 4

   
   
   

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1. View Hint View Answer Discuss in Forum

   Expression =	√32 + √48
   	√8 + √12

   
   

   =	4√2 + 4√3	=	4(√2 + √3)	= 2
   	2√2 + 2√3		2(√2 + √3)

   Correct Option: B

   Expression =	√32 + √48
   	√8 + √12

   
   

   =	4√2 + 4√3	=	4(√2 + √3)	= 2
   	2√2 + 2√3		2(√2 + √3)

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224. Simplify :	√	3	33	÷	√	9	1	× 2	√	3	1
     			64				7				9

1. 1. 45

      256

   
   
   

   2. 1	17
      	28

   
   
   

   3. 4	3
      	8

   
   
   

   4. 2	3
      	16

   
   
   

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1. View Hint View Answer Discuss in Forum

   Expression =	√	3	33	÷	√	9	1	× 2	√	3	1
   			64				7				9

   
   

   =	√	225	÷	√	64	× 2	√	28
   		64			7			9

   
   

   =	√	25	×	7	×	28	× 2
   		64		64		9

   
   

   =	5 × 7	× 2 =	35	= 2	3
   	8 × 4		16		16

   Correct Option: D

   Expression =	√	3	33	÷	√	9	1	× 2	√	3	1
   			64				7				9

   
   

   =	√	225	÷	√	64	× 2	√	28
   		64			7			9

   
   

   =	√	25	×	7	×	28	× 2
   		64		64		9

   
   

   =	5 × 7	× 2 =	35	= 2	3
   	8 × 4		16		16

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225. What is the value of	√24 + √216	?
     	√96

1. 1. 2√6

   
   
   

   2. 4√6

   
   
   

   3. 2

   
   
   

   4. 4

   
   
   

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1. View Hint View Answer Discuss in Forum

   Expression =	√24 + √216
   	√96

   
   

   =	2√6 + 6√6	=	8√6	= 2
   	4√6		4√6

   Correct Option: C

   Expression =	√24 + √216
   	√96

   
   

   =	2√6 + 6√6	=	8√6	= 2
   	4√6		4√6

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