Square Root and Cube Root - General Questions (2)

If x =	√3 + 1	and y =	√3 - 1	, then the value of (x² + y²) is:
	√3 - 1		√3 + 1

A.	10
B.	13
C.	14
D.	15

Answer: Option C

Explanation:

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

y =	(√3 - 1)	x	(√3 - 1)	=	(√3 - 1)²	=	3 + 1 - 2√3	= 2 - √3.
	(√3 + 1)		(√3 - 1)		(3 - 1)		2

x² + y² = (2 + √3)² + (2 - √3)²

= 2(4 + 3)

= 14

10.

If a = 0.1039, then the value of √4a² - 4a + 1 + 3a is:

A.	0.1039
B.	0.2078
C.	1.1039
D.	2.1039

Answer: Option C

Explanation:

√

4a² - 4a + 1 + 3a = √(1)² + (2a)² - 2 x 1 x 2a + 3a

= √(1 - 2a)² + 3a

= (1 - 2a) + 3a

= (1 + a)

= (1 + 0.1039)

= 1.1039

11.

If 3√5 + √125 = 17.88, then what will be the value of √80 + 6√5 ?

A.	13.41
B.	20.46
C.	21.66
D.	22.35

Answer: Option D

Explanation:

3√5 + √125 = 17.88

3√5 + √25 x 5 = 17.88

3√5 + 5√5 = 17.88

8√5 = 17.88

√5 = 2.235

√80 + 6√5 = √16 x 5 + 6√5

= 4√5 + 6√5

= 10√5 = (10 x 2.235) = 22.35

12.

√1.5625 = ?

A.	1.05
B.	1.25
C.	1.45
D.	1.55

Answer: Option B

Explanation:

   1|1.5625( 1.25
    |1
    |-------
  22| 56
    | 44
    |-------
 245| 1225
    | 1225
    |-------
    |    X
    |-------

√1.5625 = 1.25.

13.

The least perfect square, which is divisible by each of 21, 36 and 66 is:

A.	213444
B.	214344
C.	214434
D.	231444

Answer: Option A

Explanation:

L.C.M. of 21, 36, 66 = 2772.

Now, 2772 = 2 x 2 x 3 x 3 x 7 x 11

To make it a perfect square, it must be multiplied by 7 x 11.

So, required number = 2² x 3² x 7² x 11² = 213444

14.

What should come in place of both x in the equation	x	=	√162	.
	√128		x

A.	12
B.	14
C.	144
D.	196

Answer: Option A

Explanation:

Answer: Option A

Explanation:

Let	x	=	√162
	√128		x

Then x² = √128 x 162

= √64 x 2 x 18 x 9

= √8² x 6² x 3²

= 8 x 6 x 3

= 144.

x = √144 = 12.

15.

The cube root of .000216 is:

A.	6
B.	.06
C.	77
D.	87

Answer: Option B

Explanation:

(.000216)^1/3	=		216		1/3
			10⁶

=		6 x 6 x 6		1/3
		10² x 10² x 10²

=	6
	10²

=	6
	100

= 0.06

Square Root and Cube Root - General Questions (2)

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