SQUARE ROOT

Created: Tuesday, 13 September 2011 08:32 | Published: Tuesday, 13 September 2011 08:32 | Written by Super User | Print | Email

Introduction

In 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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