Question

1/2(8-root60+2/root5-root3

Answer 1

Answer:

√3(1+√15)/2

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Step-by-step explanation:

x=8+√60

=8+√4×15

=5+3+2√15

=(√5)²+2.√5.√3+(√3)²

=(√5+√3)²

∴, √x=√5+√3

1/√x=1/(√5+√3)

=(√5-√3)/(√5+√3)(√5-√3)

=(√5-√3)/{(√5)²-(√3)²}

=(√5-√3)/(5-3)

=(√5-√3)/2

√x+1/√x

=√5+√3+(√5-√3)/2

=(2√5+2√3+√5-√3)/2

=(3√5+√3)/2

=√3(√3.√5+1)/2

=√3(1+√15)/2