Question

simplify the following by rationalising the denominator i)6-4 root 2 /6+4 root 2

i)root 7-root 5/root 7+ root 5​

Answer 1

Answer:

(i)6-4root2/6+4root2

=(6-4root2)(6-4root2)/(6+4root2)(6-4root2)

=(6-4root2)²/(6)²-(4root2)²

=(6)²+(4root2)²-2×6×4root2/36-32

=36+32-48root2/4

=68-48root2/4

=(68/4)-(48root2)/4

=17-12root2

(ii)root7-root5/root7+root5

=(root7-root5)(root7-root5)/(root7+root5)(root7-root5)

=(root7-root5)²/(root7)²-(root5)²

=root7²+root5²-2×root7×root5/7-5

=7+5-2root35/2

=12-2root35/2

=6-root35