Question

rationalist 1/√11-3​

Answer 1

Step-by-step explanation:

multiply numerator and denominator by (√7+√3+√2)

=(√7+√3+√2)/[(√7+√3)-(√2)][(√7+√3)+(√2)]

=(√7+√3+√2)/(√7+√3)²-(√2)²

=(√7+√3+√2)/(√7)²+(√3)²+2(√7)(√3)-2

=(√7+√3+√2)/7+3+2(√21)-2

=(√7+√3+√2)/8+2(√21)

multiply numerator and denominator by 8–2(√21)

(√7+√3+√2)[8–2(√21)]/[8+2(√21)][8–2(√21)]

=(√7+√3+√2)[8–2(√21)]/[8]²-[2(√21)]²

=(√7+√3+√2)[8–2(√21)]/64–4*21

=(√7+√3+√2)[8–2(√21)]/64–84

=-(√7+√3+√2)[8–2(√21)]/20

you can solve it further

=-(√7+√3+√2)2[4–(√21)]/20

=-(√7+√3+√2)(4–√21)/10

or further

=-4√7–4√3–4√2+√21*7+√21*3+√21*2/10

=-4√7–4√3–4√2+7√3+3√7+√42/10

solving similar terms

=[-√7+3√3–4√2+√42]/10

Answer 2

Answer:

$\frac{1}{\sqrt{11} - 3}$  X$\frac{\sqrt{11} +3}{\sqrt{11} +3}$

$\frac{\sqrt{11} +3}{(\sqrt{11}) ^{2} - (3)\\^{2} }$

$\frac{\sqrt{11}+3 }{11-9}$

$\frac{\sqrt{11} +3}{2}$

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