In this page rationalizing the denominator solution1 we are going to see solution of each questions of the worksheet rationalizing the denominator.We have explained each problems with step by step explanation.
Question 1
Rationalize the denominator 1/(2 + √5)
Solution
Explanation:
In this question we have 2 + √5 in the denominator
so we have to multiply by its conjugate that is 2 - √5 with both
numerator and denominator. Now the denominator is like in the form (a+
b) (a-b). So we have simplified this using a² - b².By simplifying this
we get (√5-2)/3 as answer.
Question 2
Rationalize the denominator (6+ √5)/(6 - √5)
Solution
Explanation:
In this question we have 6 + √5 in the numerator and 6 - √5 in the denominator
so we have to multiply by its conjugate that is 6 + √5 with both
numerator and denominator. Now the denominator is like in the form (a+
b) (a-b). So we have simplified this using a² - b².In the denominator (6 + √5)². So we have expanded this using algebraic identity (a+b)² = a² + 2ab +b². By simplifying this
we get 41+ 12√5 as answer.
Question 3
Rationalize the denominator 1/(√2 + √3) and also find the
approximate value using √2 = 1.414 and √3 = 1.732
Solution
Explanation:
In this question we have √2 + √3 in the denominator so we have to multiply by its conjugate that is √2 - √3 with both numerator and denominator. Now the denominator is like in the form (a+ b) (a-b). So we have simplified this using a² - b².By simplifying this we get √3-√2 as answer.
= 1.732- 1.414
= 0.318
The approximate value of the rational number 1/√2 + √3 is 0.318.
Question 4
Rationalize the denominator (√2 + 1)/(√2 - 1)
Solution
Explanation:
In
this question we have √2 + 1 in the numerator and √2 - 1 in the
denominator
so we have to multiply by its conjugate that is √2 + 1 with both
numerator and denominator. Now the denominator is like in the form (a+
b) (a-b). So we have simplified this using a² - b².In the denominator
(√2 + 1)². So we have expanded this using algebraic identity (a+b)² = a²
+
2ab +b². By simplifying this
we get 3 - 2√2 as answer. rationalizing the denominator solution1