Chapter 11: Q23. (page 728)

Simplify.
${(1 + \sqrt{2})}^{2}$

Short Answer

Expert verified

The value of the given expression ${(1 + \sqrt{2})}^{2}$ after simplification is $3 + 2 \sqrt{2}$ .

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:

$\begin{matrix} {(1 + \sqrt{2})}^{2} = 1^{2} + 2 (1) (\sqrt{2}) + {(\sqrt{2})}^{2} (∵ {(a + b)}^{2} = a^{2} + 2 a b + b^{2}) \\ = 1 + 2 \sqrt{2} + 2 \\ = 1 + 2 + 2 \sqrt{2} \\ = 3 + 2 \sqrt{2} \end{matrix}$

Step 3. Conclusion

Therefore, the value of the given expression ${(1 + \sqrt{2})}^{2}$ after simplification is $3 + 2 \sqrt{2}$ .

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Simplify.
${(1 + \sqrt{2})}^{2}$

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.(1+2)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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Most popular questions from this chapter

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Study anywhere. Anytime. Across all devices.

Simplify.
${(1 + \sqrt{2})}^{2}$