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SQUARE ROOT

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Introduction

sqr_root_1In Math, there is always an "opposite" operation! The opposite operation for "squaring" a number is taking the "square root". ‘√’ this symbol represents “square root”.



What is squaring a number?

Term for raising a number to the 2nd power is "squaring a number".

For example:

22 = 4. This can be read as 2 "squared" equals 4. This means that 2 x 2 = 4.

And as we said earlier that square root is the opposite of squaring a number, so,


√4 = 2


The following examples help us in understanding the concept better:

1. 32 = 9                OPPOSITE IS                         √9 = 3                                      

3 squared is 9                            The Square root of 9 is 3


2. 42 = 16              OPPOSITE IS                        √16 = 4                                     

4 squared is 16                         The Square root of 16 is 4


Try This:
1. √25                                                                                    (Answer: 5)
2. √121                                                                                (Answer: 11)
3. √625                                                                                (Answer: 25)



Properties of Square Roots

1. Multiplication property for square root expression:
The product of two square roots with different numbers inside can be written in a single root with the product of those two numbers.
√a × √b =√ (a x b)

For example:

√16 × √25 = √(16 x 25)
4 × 5 = √400

20 = 20


2. Square of the number property:

When a number gets into the square root, it turns into a square of the number.
a x √b = √a2 x b

For example:

2 x √25 = √22 x 25
2 × 5 = √4 × 25
10 = √100
10 = 10


3. The square root of a fraction can be written as individual roots.

√ (a/b) = √ a / √ b

For example:

√ (25/16) = √25 / √16
5/4 = 5/4


4. When a perfect square comes out of the root, it becomes the number without square.

√(a2b) = a x √b

For example:

√(16 x 3) = √(42 x 3)
4 √3

5. Addition and subtraction property

√a + √b ≠ √ (a + b)

√16 + √25 ≠ √ (16 + 25)

4 + 5 ≠ √41

9 ≠ √41


Similarly, √ a - √b ≠ √ (a - b)

√16 - √25 ≠ √ (16 – 25)

4 – 5 ≠ √ (-9)

-1 ≠ √ (-9)



Try the following questions:

1. √(121 x4 w6 m8)                                                      (Answer: 11 x2 w3 m4)

2. √(9/25)                                                                             (Answer: 3/5)



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