# Square Root And Cube Root

Square Root And Cube Root – It define how to find, Square Root, Cube Root, Square root in division method, Trick to find square root, Find the square root and cube root in factorization method.

### Square Root

The square root of number means the factor of number bis multiple with itself , will give that number.
The above statement can be expressed by if a is the square root of b, then b is the square of a.

#### Properties Of Square Root

• Square root of a even number is even.
• Root Square of odd number is odd.
• The square root of positive number is two one is negative and another is positive.

e.g:- Square Root of 9 is -3 and +3.

• The square root of a negative number is imaginary.
• A pure square number is ending with one must be 1 or 9 in the last digit in square root.
• Square ends in 4, its square root must be end with 2 and 8.
• If a square ends in 6, its square root end with 4 and 6.
• Ending in 9, its square root end with 3 and 9.

### Trick To Finding Square Root:-

It has two type
1. Factorization Method
2. Division Method

#### Square Root inFactorization Method:-

1. Write the given number as product of prime factors.
2. Take the product of prime factors, choosing one of every pair.

#### Square Root In Division Method:-

For this method , make the pairs of  two two numbers from right side of the given number. Now, divided the first pair or number from left side, by that number, whose square is less than or equal to the pair. Again do it similarly then the quotient is the square root of the number.

### Cube Root In Factorization Method:-

The cube root of a number is that number the cube of which itself gives the given number.

#### Trick To Finding Cube Root:-

1. Express the given number in prime factorization.
2. Then take 3 pair as one and multiply then get answer.

### Question Based On Square Root And Cube Root

• Square root of 4096 is

(a) 74               (b) 64

(c) 66               (d) 63
• Square root of 0.09 is

(a) 0.03            (b) 0.13

(c) 0.3              (d) 0.5
• Volume of cube 343 cm cube, then edge of the cube is

(a) 4                 (b) 5

(c) 6                 (d) 7

• What is the square root of 2 to the power 8
(a) 6                 (b) 10
(c) 14               (d) 16
• The least number subtracted from 4931 to make perfect square

(a) 100               (b) 31

(c) 40                 (d) 81
• What is the smallest number divided by 3600 to make a perfect cube?

(a) 9                   (b) 50

(c) 300               (d) 450
• What should be added on 79 to make a perfect square ?

(a) 1                    (b) 2

(c) 3                    (d) 4
• Find the least number by which 175760 be multiplied to make it perfect cube

(a) 125               (b) 150

(c) 100               (d) 200
• The number of row and number of column are equal in a garden. Total number of tree are 5625, then what is the number of row?

(a) 85                  (b) 70

(c) 75                  (d) 90
• By what number multiplied to 21600 to make a perfect cube ?

(a) 6                    (b) 10

(c) 30                  (d) 60