To calculate: To rationalize the numerator of the expression \frac{\sqrt{

bobbie71G

bobbie71G

Answered question

2021-10-28

To calculate:
To rationalize the numerator of the expression x5x225.

Answer & Explanation

Arham Warner

Arham Warner

Skilled2021-10-29Added 102 answers

Calculation:
The numerator of a rational expression can be rationalized by removing the irrational term from it.
To remove the irrational term, the numerator and denominator of the expression are multiplied by the conjugate of the numerator.
Conjugate of an expression a+b is given as ab and vice-versa.
So the conjugate of the numerator is given as x+5.
Multiplying the numerator and the denominator with the conjugate.
x5x225=x5x225×x+5x+5
x5x225=(x5)(x+5)(x225)(x+5)
x5x225=(x)2(5)2(x225)(x+5)i.e.(a+b)(ab)=a2b2
x5x225=x5(x225)(x+5) (Since square and square root are opposite operations, they cancel out)
x5x225=x5(x5)(x+5)(x+5)i.e.(a+b)(ab)=a2b2
x5x225=1(x+5)(x+5)

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