Question

Find the value of a-b/√a+√b

Answer 1

Answer:

Your answer is √a - √b.

The process is in the image.

Answer 2

The value of a-b/√a+√b is √a -√b.

To Find:

The value of  a-b/√a+√b

Solution:

The given fraction has a radical in the denominator. So, we need to rationalize the denominator. Multiply both the denominator and numerator by √a-√b which will remove the radicals from the denominator.

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

∴ The value of a-b/√a+√b is √a -√b.

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