write-without-roots-in-denominator-if-possible-1-1-a-2-1-a-b-3-1-a-b-c-4-1-a-b-c-d-5-1-a-b-c-d-e-

Question Number 58390 by MJS last updated on 22/Apr/19

write without roots in denominator if possible

(1) \frac{1}{\sqrt{a}}

(2) \frac{1}{\sqrt{a} + \sqrt{b}}

(3) \frac{1}{\sqrt{a} + \sqrt{b} + \sqrt{c}}

(4) \frac{1}{\sqrt{a} + \sqrt{b} + \sqrt{c} + \sqrt{d}}

(5) \frac{1}{\sqrt{a} + \sqrt{b} + \sqrt{c} + \sqrt{d} + \sqrt{e}}

Commented by tanmay last updated on 22/Apr/19

s i r p l s c h e c k m y a n s w e r \dots

Commented by MJS last updated on 22/Apr/19

your answers are right, thank you

I think the 5^{th} one {isn}^{'} t possible but I^{'} m not

sure .

Answered by tanmay last updated on 22/Apr/19

1) \frac{\sqrt{a}}{a}

2) \frac{\sqrt{a} - \sqrt{b}}{a - b}

3) \frac{\sqrt{a} + \sqrt{b} - \sqrt{c}}{{(\sqrt{a} + \sqrt{b})}^{2} - c}

= \frac{\sqrt{a} + \sqrt{b} - \sqrt{c}}{a + b - c + 2 \sqrt{a} \sqrt{b}}

= \frac{(\sqrt{a} + \sqrt{b} - \sqrt{c}) (a + b - c - 2 \sqrt{a} \sqrt{b})}{{(a + b - c)}^{2} - 4 a b}

Answered by tanmay last updated on 22/Apr/19

4) \frac{(\sqrt{a} + \sqrt{b}) - (\sqrt{c} + \sqrt{d})}{a + b - c - d + 2 \sqrt{a} \sqrt{b} - 2 \sqrt{c} \sqrt{d}}

\frac{{(\sqrt{a} + \sqrt{b}) - (\sqrt{c} + \sqrt{d}} {a + b - c - d - 2 \sqrt{a} \sqrt{b} + 2 \sqrt{c d}}}{{{(a + b - c - d)}^{2} - 4 a b - 4 c d} + 8 \sqrt{a b c d}}

= \frac{{(\sqrt{a} + \sqrt{b}) - (\sqrt{c} + \sqrt{d})} {a + b - c - d - 2 \sqrt{a b} + 2 \sqrt{c d}} [{{(a + b - c - d)}^{2} - 4 a b - 4 c d} - 8 \sqrt{a b c d}}}{{{(a + b - c - d)}^{2} - 4 a b - 4 c d}^{2} - 64 a b c d}

Commented by malwaan last updated on 23/Apr/19

t r y t o s o l v e 5

p l e a s e

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