**How to find simplest rationalizing factor ? :**

Here we are going to how to find the simplest rationalizing factor.

If the product of two irrational numbers is rational, then each one is called the rationalizing factor of the other

- (a + √x) and (a + √x) are rationalizing factors of each other.
- (a + b√x) and (a - b√x) are rationalizing factors of each other.
- √x + √y and √x - √y are rationalizing factors of each other.

**Example 1 :**

Write the rationalizing factor of the following

3√2

**Solution :**

**3√2 is irrational number.**

**By multiplying **3√2 by √2, we get rational number.

= 3√2 ⋅ √2

= 3√(2 ⋅ 2)

Since we have two same numbers multiplying inside the radical, we can factor out one term.

= 3 ⋅ 2

= 6 is the rational number

Hence the rationalizing factor of 3√2 is √2.

**Example 2 :**

Write the rationalizing factor of the following

2 ∛5

**Solution :**

2 ∛5** is irrational number.**

**By multiplying **2 ∛5 by ∛25, we may get rid of the cube root.

= 2 ∛5 ⋅ ∛25

= 2 ∛(5 ⋅ 25)

= 2 ∛(5 ⋅ 5 ⋅ 5)

= 2 ⋅ 5

= 10 is rational number

Hence the rationalizing factor of 2 ∛5 is ∛25.

**Example 3 :**

Write the rationalizing factor of the following

5 - 4√3

**Solution :**

Rationalizing factor of 5 - 4√3 is 5 + 4√3

(5 - 4√3) (5 + 4√3) = 5(5) + 5(4√3) - 4√3(5) - 16(√3√3)

= 25 + 20 √3 - 20 √3 - 16 (3)

= 25 - 48

= -23 it is rational number

Hence the rationalizing factor of 5 - 4√3 is 5 + 4√3

**Example 4 :**

Write the rationalizing factor of the following

√2 + √3

**Solution :**

Rationalizing factor of √2 + √3 is √2 - √3

**Example 5 :**

Write the rationalizing factor of the following

√5 - √2

**Solution :**

Rationalizing factor of √5 - √2 is √5 + √2

**Example 6 :**

Write the rationalizing factor of the following

2 + √3

**Solution :**

Rationalizing factor of 2 + √3 is 2 - √3

Let us look into the next example on "How to find simplest rationalizing factor".

**Example 7 :**

Write the rationalizing factor of the following

√75

**Solution :**

To find the least number to be multiplied to convert √75 as rational number.We have to split 75.

√75 = √(5 ⋅ 5 ⋅ 3)

√75 ⋅ √3 = √(5 ⋅ 5 ⋅ 3) ⋅ √3

= √(5 ⋅ 5 ⋅ 3 ⋅ 3)

= 15 is the rational number

Hence √3 is the rationalizing factor of √75.

Let us look into the next example on "How to find simplest rationalizing factor".

**Example 8 :**

Write the rationalizing factor of the following

5 - 7√3

**Solution :**

Rationalizing factor of 5 - 7√3 is 5 + 7√3

- Rationalization of surds
- Comparison of surds
- Operations with radicals
- Ascending and descending order of surds
- Simplifying radical expression
- Exponents and powers

We hope that the students would have understood the stuff given on "How to find simplest rationalizing factor"

Apart from the stuff given above, if you want to know more about "How to find simplest rationalizing factor"

If you need any other stuff, please use our google custom search here.

HTML Comment Box is loading comments...

**WORD PROBLEMS**

**HCF and LCM word problems**

**Word problems on simple equations **

**Word problems on linear equations **

**Word problems on quadratic equations**

**Area and perimeter word problems**

**Word problems on direct variation and inverse variation **

**Word problems on comparing rates**

**Converting customary units word problems **

**Converting metric units word problems**

**Word problems on simple interest**

**Word problems on compound interest**

**Word problems on types of angles **

**Complementary and supplementary angles word problems**

**Markup and markdown word problems **

**Word problems on mixed fractrions**

**One step equation word problems**

**Linear inequalities word problems**

**Ratio and proportion word problems**

**Word problems on sets and venn diagrams**

**Pythagorean theorem word problems**

**Percent of a number word problems**

**Word problems on constant speed**

**Word problems on average speed **

**Word problems on sum of the angles of a triangle is 180 degree**

**OTHER TOPICS **

**Time, speed and distance shortcuts**

**Ratio and proportion shortcuts**

**Domain and range of rational functions**

**Domain and range of rational functions with holes**

**Graphing rational functions with holes**

**Converting repeating decimals in to fractions**

**Decimal representation of rational numbers**

**Finding square root using long division**

**L.C.M method to solve time and work problems**

**Translating the word problems in to algebraic expressions**

**Remainder when 2 power 256 is divided by 17**

**Remainder when 17 power 23 is divided by 16**

**Sum of all three digit numbers divisible by 6**

**Sum of all three digit numbers divisible by 7**

**Sum of all three digit numbers divisible by 8**

**Sum of all three digit numbers formed using 1, 3, 4**

**Sum of all three four digit numbers formed with non zero digits**