Chapter 8: Q.517 (page 853)

In the following exercises, simplify
$(a) 7 \sqrt{2} - 3 \sqrt{2} (b) 7 \sqrt[3]{p} + 2 \sqrt[3]{p} (c) 5 \sqrt[3]{x} - 3 \sqrt[3]{x}$

Short Answer

Expert verified

Simplifying

a) $7 \sqrt{2} - 3 \sqrt{2} = 4 \sqrt{2}$

b) $7 \sqrt[3]{p} + 2 \sqrt[3]{p} = 9 \sqrt[3]{p}$

c) $5 \sqrt[3]{x} - 3 \sqrt[3]{x} = 2 \sqrt[3]{x}$

Step by step solution

Step 1. Given information

Here we have given,

$(a) 7 \sqrt{2} - 3 \sqrt{2} (b) 7 \sqrt[3]{p} + 2 \sqrt[3]{p} (c) 5 \sqrt[3]{x} - 3 \sqrt[3]{x}$

Step 2. Concept

Here we will use,

Distributive property:

a(b + c) = ab + ac

Part (a) Step 1. Explanation

We have,

$7 \sqrt{2} - 3 \sqrt{2}$

Factoring common factor out,

$7 \sqrt{2} - 3 \sqrt{2} = \sqrt{2} (7 - 3)$

$\Rightarrow 7 \sqrt{2} - 3 \sqrt{2} = 4 \sqrt{2}$

Part (a) Step 2. Conclusion

Hence, value of radical expression $7 \sqrt{2} - 3 \sqrt{2}$ is $4 \sqrt{2}$

Part (b) Step 1. Explanation

We have,

$7 \sqrt[3]{p} + 2 \sqrt[3]{p}$

Factoring common factor out,

role="math" localid="1645081089020" $7 \sqrt[3]{p} + 2 \sqrt[3]{p} = (7 + 2) \sqrt[3]{p}$

$\Rightarrow 7 \sqrt[3]{p} + 2 \sqrt[3]{p} = 9 \sqrt[3]{p}$

Part (b) Step 2. Conclusion

Hence, value of radical expression $7 \sqrt[3]{p} + 2 \sqrt[3]{p}$ is, $9 \sqrt[3]{p}$ .

Part (c) Step 1. Explanation

We have,

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

Factoring common factor out,

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

$\Rightarrow 5 \sqrt[3]{x} - 3 \sqrt[3]{x} = 2 \sqrt[3]{x}$

Part (c) Step 2. Conclusion

Hence, value of radical expression $5 \sqrt[3]{x} - 3 \sqrt[3]{x}$ is $2 \sqrt[3]{x}$ .

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In the following exercises, simplify
$(a) 7 \sqrt{2} - 3 \sqrt{2} (b) 7 \sqrt[3]{p} + 2 \sqrt[3]{p} (c) 5 \sqrt[3]{x} - 3 \sqrt[3]{x}$

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 1. Explanation

Part (b) Step 2. Conclusion

Part (c) Step 1. Explanation

Part (c) Step 2. Conclusion

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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 1. Explanation

Part (b) Step 2. Conclusion

Part (c) Step 1. Explanation

Part (c) Step 2. Conclusion

One App. One Place for Learning.

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In the following exercises, simplify
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