Please explain how to rationalize the denominator?

Question

Please explain how to rationalize the denominator of 4 / 6 - square root of 5, explain how the denominator gets rationalized.

4
-------------------------------
6 - (square root of 5)

Answer 1

You have to multiply and divide by exactly the same quantity so it would be like multiplying times 1.. in this case your equation would look like this:

4/ 6-rs5 x 6+rs5/6+rs5 = 4 x ( 6 +rs5)/ 36 - 5 = 24+4 x rs5 / 31 = 1.062718

Answer 2

mb1

multiply the fraction by "1" in the form of

(6 + sqrt(5)) / (6 + sqrt(5))

( 4 / (6 - sqrt(5)) ) * (6 + sqrt(5)) / (6 + sqrt(5))

note that the denominator is
(6 - sqrt(5)) * (6 + sqrt(5))
= 36 - 5
= 31

this comes from the "difference of squares" fasctorization

a^2 - b^2 = (a + b)(a - b)

Answer 3

4/6 square root of 5 must be multiplied with square root of 5 / square root of 5 then u get 4 square root 5/30

Answer 4

Simply multiply the numerator and denominator by the conjugate of the denominator.

By conjugate, look at the following examples:
Conjugate of [1 + sqrt(2)] = [1 - sqrt(2)]
Conjugate of [1 - sqrt(2)] = [1 + sqrt(2)]
Conjugate of [sqrt(2) - 1] = [sqrt(2) + 1]
Conjugate of [sqrt(2) + 1] = [sqrt(2) - 1]

After multiplying, you will end up with the denominator as a whole number, because remember,
(A+B) * (A-B) = A^2 - B^2

[in which the sqrt sign is being removed in either A or B]


Now do the problem yourself.

Answer 5

4/6-root5
multiply and divide by its conjugate ie 6+root5
4/6-root5 * 6+root5/6+root5
4(6-root5)/(6-root5)(6+root5)
24-4root5/(6)^2-(root5)^2 *
24-4root 5/36-5
24-4root5/31
* note:denominator comes from formula (a+b)(a-b)=a^2-b^2

pls don't make the mistake of multiplying the term only by surd
we don't do it when there is addition or subtraction in the denominator

Answer 6

4 / (6 - √5)
= 4 / [(6 - √5)].[ (6 + √5) / (6 + √5) ]
= 4. (6 + √5) / [ 36 - 5]
= (4 /31).(6 + √5)