Rationalizing the Denominator Solution3






In this page rationalizing the denominator solution3 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 (2 + √3)/(2 - √3) = x + y √3 and find the value of x and y.

Solution

L.H.S

In this question we have 2 + √3 in the numerator and 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.In the numerator we have  (2+√3)² .This exactly matches with the formula (a+b)². We have expanded by using formula a² + 2ab + b². By simplifying this we get (7+4√3). Now we have to compare the final answer with R.H.S

By comparing this we get x =  7 and y = 4 as the final answer.


Question 2

Rationalize the denominator (5 + 4√3)/(4 + 5√3) = x + y √3 and find the value of x and y.

Solution

L.H.S

In this question we have 5 + 4√3 in the numerator and 4 + 5√3 in the denominator so we have to multiply by its conjugate that is 4 - 5 √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.In the numerator we have (5 + 4√3)(4 - 5√3) We have multiplied this using distributive property. Then we are going to combine the like terms.

By simplifying this we get (40+9√3)/59. Now we have to compare the final answer with R.H.S to get the value of x and y.rationalizing the denominator solution3 rationalizing the denominator solution3

By comparing this we get x =  40/59 and y = 9/59 as the final answer.

Quote on Mathematics

“Mathematics, without this we can do nothing in our life. Each and everything around us is math.

Math is not only solving problems and finding solutions and it is also doing many things in our day to day life.  They are: 

It subtracts sadness and adds happiness in our life.    

It divides sorrow and multiplies forgiveness and love.

Some people would not be able accept that the subject Math is easy to understand. That is because; they are unable to realize how the life is complicated. The problems in the subject Math are easier to solve than the problems in our real life. When we people are able to solve all the problems in the complicated life, why can we not solve the simple math problems?

Many people think that the subject math is always complicated and it exists to make things from simple to complicate. But the real existence of the subject math is to make things from complicate to simple.”