Question

What is rationalising factor?

Answer 1

rationalizing factor is defined as a homogenous quadratic function of some mathematical symbol. The symbols are as follows. (⋋, ∑, ∍) etc. We see that how a rationalizing factor can be obtained for a given equation. Rationalizing factor contain a root higher than a Square root.
In many cases Rationalizing Factor is easily obtained by using its conjugate by using the factor expression such as (Xp + yq).
It is a process in which the nth number in the denominator of an Irrational Function is avoided.
This nth number can be monomials or binomials. It involves square roots also.
Nth number ‘p’ is the number ‘x’ in which, when raised the power of ‘n’, equal to ‘p’ then the nth value is
Xp = p; where n is the degree of roots.
The Rationalization factor for a monomials or binomials.
Example 20/√p then the factors are
= 20/√p
= (20/√p . √p/√p)
= (20√p / √p2)
= 20√p / p.
If the number is given √3 + √ 4 + √ 6, number is in the denominator, then find its rationalizing factor.

x
√3 + √ 4 + √ 6 then the rationalization factors are,
Firstly we have to multiply the conjugate of this number.
X √3 + √ 4 - √ 6
√3 + √ 4 + √ 6 X √3 + √ 4 - √ 6 ;
On multiplying the equation we get the new equation as,
= x(√3 + √ 4 - √ 6 )
(√3 + √ 4 )2 - (√ 6 ) 2

= x(√3 + √ 4 - √ 6 )
(√3 + √ 4 + √ 6 ) (√3 + √ 4 - √ 6 );
This value solve by equation by a2 –b2 = (a + b) (a - b).

Answer 2

here is a simpler explanation: The term with which you multiply and divide to make the whole term rational (i.e denominator rational)
e.q. rationalising factor for (1/(sqrt(2) - 1) is (sqrt(2) +1 ) as when multiplied and divided by this,, we are left with (sqrt(2) + 1)/1 which is rational

Answer 3

that's rationalizing factor