Chapter 8: Q. 8.89 (page 795)

Simplify-
(a) ${(10 + \sqrt{2})}^{2}$
(b) ${(1 + 3 \sqrt{6})}^{2}$

Short Answer

Expert verified

The values are-

(a) $102 + 20 \sqrt{2}$

(b) $55 + 6 \sqrt{6}$

Step by step solution

Step 1. Explanation

(a) and (b) We can identify the property of addition here, i.e., ${(a + b)}^{2}$ .

We know that ${(a + b)}^{2} = a^{2} + 2 a b + b^{2}$ .

By applying it, we will get the values.

Step 2. Solving for part (a)

We have ${(10 + \sqrt{2})}^{2}$ .

Applying the property of ${(a + b)}^{2}$ will give us,

role="math" localid="1644765602873" $= {(10 + \sqrt{2})}^{2} = {(10)}^{2} + (2 \cdot 10 \cdot \sqrt{2}) + {(\sqrt{2})}^{2} = 100 + 20 \sqrt{2} + 2 = 102 + 20 \sqrt{2}$

Thus we get the value as $102 + 20 \sqrt{2}$ .

Step 3. Solving for part (b)

We have ${(1 + 3 \sqrt{6})}^{2}$ .

Applying the property of ${(a + b)}^{2}$ will give us,

role="math" localid="1644765862716" $= {(1 + 3 \sqrt{6})}^{2} = {(1)}^{2} + (2 \cdot 1 \cdot 3 \sqrt{6}) + {(3 \sqrt{6})}^{2} = 1 + 6 \sqrt{6} + 54 = 55 + 6 \sqrt{6}$

Thus we get the value as $55 + 6 \sqrt{6}$ .

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Simplify-
(a) ${(10 + \sqrt{2})}^{2}$
(b) ${(1 + 3 \sqrt{6})}^{2}$

Short Answer

Step by step solution

Step 1. Explanation

Step 2. Solving for part (a)

Step 3. Solving for part (b)

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Applied Mathematics

Theoretical and Mathematical Physics

Mechanics Maths

Discrete Mathematics

Probability and Statistics

Study anywhere. Anytime. Across all devices.

Simplify-(a)(10+2)2(b)(1+36)2

Short Answer

Step by step solution

Step 1. Explanation

Step 2. Solving for part (a)

Step 3. Solving for part (b)

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Applied Mathematics

Theoretical and Mathematical Physics

Mechanics Maths

Discrete Mathematics

Probability and Statistics

Study anywhere. Anytime. Across all devices.

Simplify-
(a) ${(10 + \sqrt{2})}^{2}$
(b) ${(1 + 3 \sqrt{6})}^{2}$