Question

Rationalize: 2/3-root 5

Answer 1

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Answer 2

Answer:

3 + root5/2

Step-by-step explanation:

To rationalize 2/3 - root5

Step 1 = multiply both the numerator and the denominator of the number with the conjugate of the denominator(3 - root5)

The conjugate of the numbers's denominator is 3 + root5

So,

= 2/3 - root5 X 3 + root5/3 + root5

Step 2 = Follow the identity

After multiplying-

= 6 + 2 root5/(3)^2 - (root5)^2[using identity A^2 - B^2 =(A + B)(A - B)

Then,

= 6 + 2 root5/9[3^2] - 5[root5 X root5]

= 6 + 2 root5/4

= 3 + root5/2