Question

Rationalize the denominator 5/root7 -3

Answer 1

Given :

$\frac{5}{ \sqrt{7} - 3 }$

Formulae used :

$1) \: \: (x + y)(x - y) = x {}^{2} - y {}^{2} \\ 2) \: \: ( \sqrt{x} ) {}^{2} = x$

What to do = rationalisation of the denominator.

Solution :

Concept :

Step 1: To rationalize the denominator, you must multiply both the numerator and the denominator by the conjugate of the denominator. Remember to find the conjugate all you have to do is change the sign between the two terms.

Step 2: Distribute (or FOIL) both the numerator and the denominator. Remember that you can multiply numbers outside the radical with numbers outside the radical and numbers inside the radical with numbers inside the radical.

Step 3: Combine like terms.

Step 4: Simplify the radicals.

Step 5: Combine like terms.

Step 6: Reduce or add the fraction, if you can.

Answer

$\frac{5}{ \sqrt{7} - 3} \\ take \: minus \: ( - ) \: common \: to \: avoid \: negative \: denominator \\ \frac{5}{3 - \sqrt{7} } \times \frac{3 + \sqrt{7} }{3 + \sqrt{7} } \\ \frac{15 + 5 \sqrt{7} }{9 - 7} \\ \frac{15 + 5 \sqrt{7} }{2} \: \: </u><u>A</u><u>nswer$