__Rules and Methods of Square Root and Cube Root Download in PDF:__
Dear Readers, here we have given rules and methods of Square root and cube root for the upcoming SSC CGL and Railway Exams. Candidates those who are preparing for the examinations can use this material.

__Square Root and Cube Root__- Download

__Rules and Methods of Square Root and Cube Root__

__Square__
When a number is multiplied by itself, the
product is called the square of the number.

(i.e.,) 2 × 2, we get 4, we say that 4 is the
square of 2.

__Square Root__
The square root of a given number is that
number which when multiplied by itself is equal to the given number.

e.g., 2

^{2}= 4
Therefore, 2 is the square root of 4 and write
it as 2 = √4

__Cube__
When a number is multiplied by itself thrice,
the product is called the cube of the number.

(i.e.,) 3 × 3 × 3, we get 27, so we can say
that 27 is the cube of 3.

__Cube Root__
Cube Root of a given number is the number
which when raised to the third power will produce the given number. Thus, 4

^{3}= 64, hence 64 has a cube root of 4. The symbol^{3}√ is used to denote the cube root.
Eg.,

^{3}√64 = 4

^{3}√125 = 5

We have find the cube root by factorization
method For find the cube root, make groups of three and take one out of every
group.

Eg.,

^{3}√1728
=

^{3}√(2 × 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3 × 3 × 3)
=
2 × 2 × 3

=
12

**Important Facts :**

·
√ab = √a ×√b

·
√(a / b) = √a / √b

·
The value of √ x ∓ √x ∓ √x ∓ …..∞

Suppose
‘a’ and ‘b’ are consecutive factors of x where b > a. If there sign is (+)
in the expression, the answer is b (i.e) bigger factor and if there sign is
(-), the answer is a i.e., the smaller factor.

Example
√20 - √20 - √20 - √20 … . ∞ is equal to

Sol.
20 = 4 × 5

Since,
the sign is (-), then the required answer is the smaller factor i.e., 4

·
√x. √ x. √ x. √ x. … .∞ If the root goes upto ∞ in multiplication, the answer is x itself

**Solved Examples**

**1).**If √1369 = 37; find the value of √13.69 + √0.1369 + √0.001369 + √0.00001369

a)
4.1017

b)
4.1107

c)
4.0117

d)
4.0017

**2).**Find the smallest number which should be added to 8958 so that the sum is a perfect square

a)
47

b)
67

c)
63

d)
57

**3).**What is the smallest number to be subtracted from 549162 in order to make it a perfect square?

a)
91

b)
81

c)
71

d)
101

**4).**Find the value of n, if √3

^{n}= 729

a)
14

b)
12

c)
16

d)
18

**5).**Find the value

^{3}√1 – (91 / 216)

a)
1 / 6

b)
5 / 6

c)
5 / 7

d)
2 / 7

__Answers__**:**

**1). b) 2). b) 3). b) 4). b) 5). b)**

__Solution:__**1).**Given expression = √(1369 / 100) + √(1369 / 10000) + √(1369 / 1000000) + √(1369 / 100000000)

=
(37 / 10) + (37 / 100) + (37 / 1000) + (37 / 10000)

=
3.7 + 0.37 + 0.037 + 0.0037 = 4.1107

**Answer: b)**

**2).**

Required number = (95)

^{2}– 8958 = 9025 – 8958 = 67**Answer: b)**

**3).**

Required number to be subtracted = 81

**Answer: b)**

**4).**√3

^{n}= 729

√3

^{n}= √3^{6}
3

^{n}= (3^{6})^{2}
3

^{n}= 3^{12}
n = 12

**Answer: b)**

**5).**

^{3}√(216 – 91) / 216)

=

^{3}√(125 / 216)
=

^{3}√(5 × 5 × 5) / (6 × 6 × 6) = 5 / 6**Answer: b)**