Question

Rationalising factor of a1/3+ b1 /3 is -

Answer 1

The rationalising factor is (a power 2/3-a power 1/3. b power 1/3+ b power 2/3)

Answer 2

Answer:

Rationalizing factor of $a^{1/3}+b^{1/3}$ = $a^{2/3}+b^{2/3} -a^{1/3}b^{1/3}$

Step-by-step explanation:

Given irrational expression is $a^{1/3}+b^{1/3}$

To find,

The rationalizing factor

Recall the concept

The rationalizing factor of an irrational number is that expression with which the irrational number is multiplied to get a rational number

Let us take the irrational number  $a^{2/3}+b^{2/3} -a^{1/3}b^{1/3}$

Multiply this irrational number with  $a^{1/3}+b^{1/3}$ we get,

($a^{1/3}+b^{1/3}$)( $a^{2/3}+b^{2/3} -a^{1/3}b^{1/3}$)

= $a^{1/3}(a^{2/3}+b^{2/3} -a^{1/3}b^{1/3}) +b^{1/3} (a^{2/3}+b^{2/3} -a^{1/3}b^{1/3})$

= $a^{1/3+2/3} +a^{1/3}b^{2/3}-a^{1/3+1/3}b^{1/3} + b^{1/3}a^{2/3}+b^{1/3+2/3}-a^{1/3}b^{2/3}$

= $a +a^{1/3}b^{2/3}-a^{2/3}b^{1/3} + b^{1/3}a^{2/3}+b-a^{1/3}b^{2/3}$

= a+b

Since a+b is a rational number, we can say that  $a^{2/3}+b^{2/3} -a^{1/3}b^{1/3}$ is the rationalizing factor of  $a^{1/3}+b^{1/3}$

∴Rationalizing factor of $a^{1/3}+b^{1/3}$ =   $a^{2/3}+b^{2/3} -a^{1/3}b^{1/3}$

#SPJ3