Chapter 11: Q.520 (page 1069)

In the following exercises, simplify
$(a) \sqrt{80 c^{7}} - \sqrt{20 c^{7}} (b) 2 \sqrt[4]{162 r^{10}} + 4 \sqrt[4]{32 r^{10}}$

Short Answer

Expert verified

Simplifying,

$(a) \sqrt{80 c^{7}} - \sqrt{20 c^{7}} = 2 \sqrt{5} c^{3} \sqrt{c} (b) 2 \sqrt[4]{162 r^{10}} + 4 \sqrt[4]{32 r^{10}} = 14 \sqrt[4]{2} r^{2} \sqrt[4]{r^{2}}$

Step by step solution

Step 1. Given information

We have given,

$(a) \sqrt{80 c^{7}} - \sqrt{20 c^{7}} (b) 2 \sqrt[4]{162 r^{10}} + 4 \sqrt[4]{32 r^{10}}$

Step 2. Concept

Here we are going to factor the number inside the radical such that at least on of them is perfect square.

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

Here we are going to apply radical rule,

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

Part (a) Step 1. Explanation

We have,

$\sqrt{80 c^{7}} - \sqrt{20 c^{7}}$

Simplifying it,

$\sqrt{80 c^{7}} - \sqrt{20 c^{7}} = \sqrt{16 \times 5} \cdot \sqrt{c {(c^{3})}^{2}} - \sqrt{4 \times 5} \cdot \sqrt{c {(c^{3})}^{2}}$

$\Rightarrow \sqrt{80 c^{7}} - \sqrt{20 c^{7}} = 4 \sqrt{5} c^{3} \sqrt{c} - 2 \sqrt{5} c^{3} \sqrt{c}$

$\Rightarrow \sqrt{80 c^{7}} - \sqrt{20 c^{7}} = 2 \sqrt{5} c^{3} \sqrt{c} (2 - 1)$

$\Rightarrow \sqrt{80 c^{7}} - \sqrt{20 c^{7}} = 2 \sqrt{5} c^{3} \sqrt{c}$

Part (a) Step 2. Conclusion

Hence, value of $\sqrt{80 c^{7}} - \sqrt{20 c^{7}}$ is $2 \sqrt{5} c^{3} \sqrt{c}$ .

Part (b) Step 1. Explanation

We have,

$2 \sqrt[4]{162 r^{10}} + 4 \sqrt[4]{32 r^{10}}$

Simplifying it ahead,

localid="1663690168534" $2 \sqrt[4]{162 r^{10}} + 4 \sqrt[4]{32 r^{10}} = 2 \sqrt[4]{162} \sqrt[4]{r^{10}} + 4 \sqrt[4]{32} \sqrt[4]{r^{10}} = 2 \cdot 3 \sqrt[4]{2} r^{2} \sqrt[4]{r^{2}} + 4 \cdot 2 \sqrt[4]{2} r^{2} \sqrt[4]{r^{2}} = 6 \sqrt[4]{2} r^{2} \sqrt[4]{r^{2}} + 8 \sqrt[4]{2} r^{2} \sqrt[4]{r^{2}} = 14 \sqrt[4]{2} r^{2} \sqrt[4]{r^{2}}$

Part (b) Step 2. Conclusion

Hence, value of $2 \sqrt[4]{162 r^{10}} + 4 \sqrt[4]{32 r^{10}}$ is $14 \sqrt[4]{2} r^{2} \sqrt[4]{r^{2}}$ .

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In the following exercises, simplify
$(a) \sqrt{80 c^{7}} - \sqrt{20 c^{7}} (b) 2 \sqrt[4]{162 r^{10}} + 4 \sqrt[4]{32 r^{10}}$

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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In the following exercises, simplify(a)80c7-20c7(b)2162r104+432r104

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

One App. One Place for Learning.

Most popular questions from this chapter

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In the following exercises, simplify
$(a) \sqrt{80 c^{7}} - \sqrt{20 c^{7}} (b) 2 \sqrt[4]{162 r^{10}} + 4 \sqrt[4]{32 r^{10}}$