Chapter 8: Q.527 (page 854)

In the following exercises, multiply.
${a) (4 + \sqrt{11})}^{2} b) {(3 - 2 \sqrt{5})}^{2}$

Short Answer

Expert verified

Simplifying,

${a) (4 + \sqrt{11})}^{2} = 27 + 8 \sqrt{11} b) {(3 - 2 \sqrt{5})}^{2} = 29 - 12 \sqrt{5}$

Step by step solution

Step 1. Given information

We have given,

${a) (4 + \sqrt{11})}^{2} b) {(3 - 2 \sqrt{5})}^{2}$

Step 2. Concept

Here we are going to use perfect square formula,

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

Part (a) Step 1. Explanation

We have,

${(4 + \sqrt{11})}^{2}$

Using perfect square formula,

$4^{2} + 2 \cdot 4 \sqrt{11} + {(\sqrt{11})}^{2}$

Simplifying and adding,

$27 + 8 \sqrt{11}$

Part (a) Step 2. Conclusion

Hence, simplifying ${(4 + \sqrt{11})}^{2}$ we will get,

$27 + 8 \sqrt{11}$ .

Part (b) Step 1. Explanation

We have,

${(3 - 2 \sqrt{5})}^{2}$

Using perfect square formula,

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

Simplifying and adding,

$29 - 12 \sqrt{5}$

Part (b) Step 2. Conclusion

Hence, simplifying ${(3 - 2 \sqrt{5})}^{2}$ we will get $29 - 12 \sqrt{5}$ .

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In the following exercises, multiply.
${a) (4 + \sqrt{11})}^{2} b) {(3 - 2 \sqrt{5})}^{2}$

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, multiply.a)(4+11)2b)3-252

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

Recommended explanations on Math Textbooks

Mechanics Maths

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Theoretical and Mathematical Physics

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Study anywhere. Anytime. Across all devices.

In the following exercises, multiply.
${a) (4 + \sqrt{11})}^{2} b) {(3 - 2 \sqrt{5})}^{2}$