Question

what is rationalising factor of 2/3√5​

Answer 1

Question:

what is rationalising factor of 2/3√5

Solution:

$\frac{2}{3 \sqrt{5} }$

Multiplying both numerator and denominator with√5

Therefore:

$\frac{2 \times \sqrt{5} }{3 \times \sqrt{5} \times \sqrt{5} }$

$= \frac{2 \sqrt{5} }{3 \times 5} \\ = \frac{2 \sqrt{5} }{15}$

Answer 2

Step-by-step explanation:

(2+

3

+

5

)(2+

3

−

5

)=(2+

3

)

2

−(

5

)

2

=4+3+4

3

−5=7+4

3

−5

=2+4

3

=2(1+2

3

)

Now, conjugate of factor 1+2

3

is 1−2

3

=(1+2

3

)(1−2

3

)=1

2

−(2

3

)

2

=1−4×3=−11

∴(2+

3

+

5

)(2+

3

−

5

)(1−2

3

)

=2(1+2

3

)(1−2

3

)

=2(1

2

−(2

3

)

2

)=2(1−12)=−22,which is rational

Hence, (2+

3

−

5

)(1−2

3

) is the simplest rationalising factor of 2+

3

+

5