Tricks to Solve Problems on Square Root & Cube Root

Square Root

If x2 = y,

we say that the square root of y is x and we write y = (+/-)x

Thus, 4 = 2, -2

9 = 3, -3

196 = 14, -14

Cube Root:

The cube root of a given number x is the number whose cube is x.

We, denote the cube root of x by 3√x.

Thus,  3√8 = 2 x 2 x 2 = 2,

3√343 = 7 x 7 x 7 = 7 etc.

Note:

  • 1. xy = x    x    y

    2.
    x
    y
    = x = x x y = xy .
    y y y y

 

 

Problems on Square Root & Cube Root

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

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.

If √35 + √125 = 17.88, then what will be the value of√ 80 + √65 ?

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

A group of students decided to collect as many paise from each member of group as is the number of members. If the total collection amounts to Rs. 59.29, the number of the member is the group is:

How many two-digit numbers satisfy this property.: The last digit (unit's digit) of the square of the two-digit number is 8 ?

The square root of 64009 is:

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