The value of 1/\sqrt{12-\sqrt140} -1/\sqrt{8-\sqrt60} -2/\sqrt{10+\sqrt84}+1 is:

SSC CGL Model Paper 11

Question : 57 of 100

Marks: +1, -0

The value of

1/√{12-√140}

-1/√{8-√60}

-2/√{10+√84}+1

is:

Solution:

1/√{12-√140}

=1/{√{7+5-√{4×7×5}}}

=1/{√{ (√7-√5)^2}

={√7+√5}/2

1/√{8-√60}

=1/√{7+3-√{4×5×3}}

={√5+√3}/2

2/√{10+√84}

=2/√{7+3+√{4×7×3}}

=(√7-√3)/2

So, combining all parts, we get

={√7+√5-√5-√3-√7+√3}/2+1

=0+1=1

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