Chapter 8: Q.537 (page 854)

In the following exercises, simplify.
$\frac{\sqrt{x} + \sqrt{8}}{\sqrt{x} - \sqrt{8}}$

Short Answer

Expert verified

Simplifying,

$\frac{\sqrt{x} + \sqrt{8}}{\sqrt{x} - \sqrt{8}} = \frac{x + 4 \sqrt{2 x} + 8}{x - 8}$

Step by step solution

Step 1. Given information

We have given,

$\frac{\sqrt{x} + \sqrt{8}}{\sqrt{x} - \sqrt{8}}$

Step 2. Concept

To rationalize the denominator we need to multiply numerator and denominator by a conjugate of the denominator.

Then we will use the difference of two squares formula and distributive property to simplify it ahead,

Distributive property,

a(b + c) = ab + ac.

Difference of two squares formula,

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

Step 3. Explanation

We have,

$\frac{\sqrt{x} + \sqrt{8}}{\sqrt{x} - \sqrt{8}}$

Multiplying numerator and denominator by conjugate of $\sqrt{x} - \sqrt{8}$ ,

$\frac{(\sqrt{x} + \sqrt{8}) (\sqrt{x} + \sqrt{8})}{(\sqrt{x} - \sqrt{8}) (\sqrt{x} + \sqrt{8})}$

Using difference of two squares formula and distributive property,

$\frac{x + 2 \sqrt{8 x} + 8}{x - 8}$

$\Rightarrow \frac{x + 4 \sqrt{2 x} + 8}{x - 8}$

Step 4. Conclusion

Hence, rationalizing and simplifying $\frac{\sqrt{x} + \sqrt{8}}{\sqrt{x} - \sqrt{8}}$ we will get, $\frac{x + 4 \sqrt{2 x} + 8}{x - 8}$ .

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In the following exercises, simplify.
$\frac{\sqrt{x} + \sqrt{8}}{\sqrt{x} - \sqrt{8}}$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Concept

Step 3. Explanation

Step 4. Conclusion

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In the following exercises, simplify.x+8x-8

Short Answer

Step by step solution

Step 1. Given information

Step 2. Concept

Step 3. Explanation

Step 4. Conclusion

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Geometry

Discrete Mathematics

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Applied Mathematics

Pure Maths

Study anywhere. Anytime. Across all devices.

In the following exercises, simplify.
$\frac{\sqrt{x} + \sqrt{8}}{\sqrt{x} - \sqrt{8}}$