Question

Express the following with rational denominator ​

Answer 1

Answer:

$17-12\sqrt{2}$

Step-by-step explanation:

multiply both numerator and denominator with the conjugate of (6+4root2)

$\frac{6-4\sqrt{2} }{6+4\sqrt{2} } *\frac{6-4\sqrt{2}}{6-4\sqrt{2}}$

then you will get

$\frac{(6-4\sqrt{2})^{2} }{(6+4\sqrt{2})(6-4\sqrt{2})}$

which will give us

$\frac{(6-4\sqrt{2})^{2} }{6^{2}-(4\sqrt{2} )^{2}}$

therefore

$\frac{36-24\sqrt{2}+32 }{36-32}$

finally

$\frac{68-48\sqrt{2} }{4}$

simplified to

$17-12\sqrt{2}$

Answer 2

Answer:

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