Chapter 8: Q.525 (page 853)

In the following exercises, multiply
$a) (3 - 2 \sqrt{7}) (5 - 4 \sqrt{7}) b) (\sqrt[3]{x} - 5) (\sqrt[3]{x} - 3)$

Short Answer

Expert verified

Simplifying,

$a) (3 - 2 \sqrt{7}) (5 - 4 \sqrt{7}) = 71 - 22 \sqrt{7} b) (\sqrt[3]{x} - 5) (\sqrt[3]{x} - 3) = {(\sqrt[3]{x})}^{2} - 8 \sqrt[3]{x} + 15$

Step by step solution

Step 1. Given information

We have given,

a) (3 - 2 \sqrt{7}) (5 - 4 \sqrt{7}) b) (\sqrt[3]{x} - 5) (\sqrt[3]{x} - 3)

Step 2. Concept

Here we will going to use FOIL method,

$(a + b) (c + d) = a c + a d + b c + b d$

and radical rules,

$\sqrt[n]{a} \sqrt[n]{b} = \sqrt[n]{a b}$

$\sqrt[n]{a^{n}} = a$

Part (a) Step 1. Explanation

We have,

$(3 - 2 \sqrt{7}) (5 - 4 \sqrt{7})$

Using FOIL method,

$3 \cdot 5 + 3 (- 4 \sqrt{7}) - 2 \sqrt{7} \cdot 5 - 2 \sqrt{7} (- 4 \sqrt{7})$

Using radical rule,

$15 - 12 \sqrt{7} - 10 \sqrt{7} + 56$

$\Rightarrow 71 - 22 \sqrt{7}$

Part (a) Step 2. Conclusion

Hence, multiplying and simplifying $(3 - 2 \sqrt{7}) (5 - 4 \sqrt{7})$ we will get,

$71 - 22 \sqrt{7}$

Part (b) Step. Explanation

We have,

$(\sqrt[3]{x} - 5) (\sqrt[3]{x} - 3)$

Using FOIL method,

$\sqrt[3]{x} \sqrt[3]{x} + \sqrt[3]{x} (- 3) - 5 \sqrt[3]{x} - 5 (- 3)$

Using radical rule,

${(\sqrt[3]{x})}^{2} - 8 \sqrt[3]{x} + 15$

Part (b) Step 2. Conclusion

Hence, multiplying and simplifying $(\sqrt[3]{x} - 5) (\sqrt[3]{x} - 3)$ we will get,

${(\sqrt[3]{x})}^{2} - 8 \sqrt[3]{x} + 15$ .

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In the following exercises, multiply
$a) (3 - 2 \sqrt{7}) (5 - 4 \sqrt{7}) b) (\sqrt[3]{x} - 5) (\sqrt[3]{x} - 3)$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Concept

Part (a) Step 1. Explanation

Part (a) Step 2. Conclusion

Part (b) Step. Explanation

Part (b) Step 2. Conclusion

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Part (a) Step 2. Conclusion

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Part (b) Step 2. Conclusion

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