Question

Rationalising factor of
$a + \sqrt[3]{b}$


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Answer 1

I AM SORRY I DON'T KNOW THE ANSWER BUT GOOD NIGHT GUYS

Answer 2

Step-by-step explanation:

Given :-

a+³√b

To find:-

Find the Rationalising factor of the given number ?

Solution:-

Given number = a+³√b

It can be written as ³√(a)³+ ³√b

= (a³)⅓ + b⅓

On multiplying with (a³)⅔-a³b⅓+b⅔ then

=> [(a³)⅓ + b⅓][(a³)⅔-a³b⅓+b⅔]

It is in the form (x+y)(x²-xy+y²)

Where , x = (a³)⅓ and y = b⅓

We know that

x³+y³ = (x+y)(x²-xy+y²)

[(a³)⅓ + b⅓][(a³)⅔-a³b⅓+b⅔]

=> [(a³)⅓]³+(b⅓)³

=> a³ + b

The Rationalising factor = (a³)⅔-a³b⅓+b⅔

=> a-a³b⅓+b⅔

Answer:-

The Rationalising factor of a+³√b is a-a³b⅓+b⅔

Used formulae:-

• x³+y³ = (x+y)(x²-xy+y²)
• The product of two irrational numbers is a rational number then they are called Rationalising factors of to each other.
• The Rationalising factor of a+√b is a-√b.
• An irrational number have so many Rationalising factors
• (a^m)^n = a^(mn)