How do you rationalize the denominator and simplify $\frac{1}{\sqrt{a} + \sqrt{b}}$ $1/(sqrta+sqrtb)$ ?

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How do you rationalize the denominator and simplify $\frac{1}{\sqrt{a} + \sqrt{b}}$ $1/(sqrta+sqrtb)$ ?

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Answer 1 · 2016-03-12T22:18:25

$= \frac{\sqrt{a} - \sqrt{b}}{a - b}$ $=(sqrt(a)-sqrt(b))/(a-b)$

Explanation:

Given: $\frac{1}{\sqrt{a} + \sqrt{b}}$ $" "1/(sqrt(a)+sqrt(b))$

Known: $(a^{2} - b^{2}) = (a + b) (a - b)$ $(a^2-b^2)=(a+b)(a-b)$

So using the above known information multiply by 1 but in the form of $1 = \frac{\sqrt{a} - \sqrt{b}}{\sqrt{a} - \sqrt{b}}$ $1=(sqrt(a)-sqrt(b))/(sqrt(a)-sqrt(b))$

So
$= \frac{1}{\sqrt{a} - \sqrt{b}} \times \frac{\sqrt{a} - \sqrt{b}}{\sqrt{a} - \sqrt{b}}$ $=1/(sqrt(a)-sqrt(b)) xx (sqrt(a)-sqrt(b))/(sqrt(a)-sqrt(b))$

$= \frac{\sqrt{a} - \sqrt{b}}{a - b}$ $=(sqrt(a)-sqrt(b))/(a-b)$

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How do you rationalize the denominator and simplify $\frac{1}{\sqrt{a} + \sqrt{b}}$ $1/(sqrta+sqrtb)$ ?

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How do you rationalize the denominator and simplify 1√a+√b1/(sqrta+sqrtb)?

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How do you rationalize the denominator and simplify $\frac{1}{\sqrt{a} + \sqrt{b}}$ $1/(sqrta+sqrtb)$ ?