Chapter 8: Q. 518 (page 853)

In the following exercises, simplify
$(a) \sqrt{11 b} - 5 \sqrt{11 b} + 3 \sqrt{11 b} (b) 8 \sqrt[4]{11 c d} + 5 \sqrt[4]{11 c d} - 9 \sqrt[4]{11 c d}$

Short Answer

Expert verified

$(a) \sqrt{11 b} - 5 \sqrt{11 b} + 3 \sqrt{11 b} = - \sqrt{11} \sqrt{b} (b) 8 \sqrt[4]{11 c d} + 5 \sqrt[4]{11 c d} - 9 \sqrt[4]{11 c d} = 4 \sqrt[4]{11 c d}$

Step by step solution

Step 1. Given information

We have given,

$(a) \sqrt{11 b} - 5 \sqrt{11 b} + 3 \sqrt{11 b} (b) 8 \sqrt[4]{11 c d} + 5 \sqrt[4]{11 c d} - 9 \sqrt[4]{11 c d}$

Step 2. Concept

Here we are going to factor greatest common factor out.

Part (a) Step 1. Explanation

We have,

$\sqrt{11 b} - 5 \sqrt{11 b} + 3 \sqrt{11 b}$

Factoring our common factor,

$\sqrt{11 b} - 5 \sqrt{11 b} + 3 \sqrt{11 b} = (1 - 5 + 3) \sqrt{11 b}$

$\Rightarrow \sqrt{11 b} - 5 \sqrt{11 b} + 3 \sqrt{11 b} = - \sqrt{11} \sqrt{b}$

Part (a) Step 2. Conclusion

Hence, value of $\sqrt{11 b} - 5 \sqrt{11 b} + 3 \sqrt{11 b}$

is $- \sqrt{11} \sqrt{b}$ .

Part (b) Step 1. Explanation

We have,

$8 \sqrt[4]{11 c d} + 5 \sqrt[4]{11 c d} - 9 \sqrt[4]{11 c d}$

Factoring out common factor,

$8 \sqrt[4]{11 c d} + 5 \sqrt[4]{11 c d} - 9 \sqrt[4]{11 c d} = (8 + 5 - 9) \sqrt[4]{11 c d}$

$\Rightarrow 8 \sqrt[4]{11 c d} + 5 \sqrt[4]{11 c d} - 9 \sqrt[4]{11 c d} = 4 \sqrt[4]{11 c d}$

Part (b) Step 2. Conclusion

Hence, value of $8 \sqrt[4]{11 c d} + 5 \sqrt[4]{11 c d} - 9 \sqrt[4]{11 c d}$ is $4 \sqrt[4]{11 c d}$ .

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In the following exercises, simplify
$(a) \sqrt{11 b} - 5 \sqrt{11 b} + 3 \sqrt{11 b} (b) 8 \sqrt[4]{11 c d} + 5 \sqrt[4]{11 c d} - 9 \sqrt[4]{11 c d}$

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

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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

One App. One Place for Learning.

Most popular questions from this chapter

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In the following exercises, simplify
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