Chapter 11: Q22. (page 728)

Simplify
${(4 - \sqrt{5})}^{2}$

Short Answer

Expert verified

The value of the given expression ${(4 - \sqrt{5})}^{2}$ after simplification is $21 - 8 \sqrt{5}$ .

Step by step solution

Step 1. Write the identity of (a−b)2.

The identity of ${(a - b)}^{2}$ is:

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

Step 2. Simplify the given expression.

The value of the given expression after simplification is:

$\begin{matrix} {(4 - \sqrt{5})}^{2} = 4^{2} - 2 (4) (\sqrt{5}) + {(\sqrt{5})}^{2} (∵ {(a - b)}^{2} = a^{2} - 2 a b + b^{2}) \\ = 16 - 8 \sqrt{5} + 5 \\ = 16 + 5 - 8 \sqrt{5} \\ = 21 - 8 \sqrt{5} \end{matrix}$

Step 3. Conclusion

Therefore, the value of the given expression ${(4 - \sqrt{5})}^{2}$ after simplification is $21 - 8 \sqrt{5}$ .

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Simplify
${(4 - \sqrt{5})}^{2}$

Short Answer

Step by step solution

Step 1. Write the identity of (a−b)2.

Step 2. Simplify the given expression.

Step 3. Conclusion

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Simplify(4−5)2

Short Answer

Step by step solution

Step 1. Write the identity of (a−b)2.

Step 2. Simplify the given expression.

Step 3. Conclusion

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Mechanics Maths

Discrete Mathematics

Statistics

Probability and Statistics

Geometry

Study anywhere. Anytime. Across all devices.

Simplify
${(4 - \sqrt{5})}^{2}$