Question

Can someone please help with this math question:)

Answer 1

Solution:

The rationalisation factor for $\frac{1}{ a - \sqrt{b} }$ is $a + \sqrt{b}$

So, let us apply it here.

$\frac{1}{5 - \sqrt{2} }$

The rationalising factor for 5 - √2 is 5 + √2.

Therefore, multiplying and dividing by 5 + √2, we have

$= \frac{1}{5 - \sqrt{2} } \times \frac{5 + \sqrt{2} }{5 + \sqrt{2} } \\ = \frac{5 + \sqrt{2} }{(5 - \sqrt{2})(5 + \sqrt{2} ) } \\ = \frac{5 + \sqrt{2} }{ {(5)}^{2} - ( \sqrt{2})^{2} } \\ = \frac{5 + \sqrt{2} }{25 - 2} \\ = \frac{5 + \sqrt{2} }{23}$

Answer:

$\frac{5 + \sqrt{2} }{23}$

Hope you could understand.

If you have any query, feel free to ask.

Answer 2

Answer:

$\frac{5+\sqrt{2} }{23}$

Step-by-step explanation:

To rationalise the denominator, multiply the numerator and denominator by the conjugate of the denominator.

the conjugate of 5 - $\sqrt{2}$ is 5 + $\sqrt{2}$ , then

= $\frac{1(5+\sqrt{2}) }{(5-\sqrt{2})(5+\sqrt{2}) }$ ← expand denominator using aFOIL

= $\frac{5+\sqrt{2} }{25-2}$

= $\frac{5+\sqrt{2} }{23}$