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Exercises Roots and quadratic equations

Example 9.56 from Elementary Algebra, 9.4 Multiply Square Roots

Multiply Square Roots: example 9.56

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

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

1
Solution
Be sure to include the $2 a b$ term when squaring a binomial.
1. ⓐ
  
  Multiply using the binomial square pattern.
  
  Simplify.
  
  Combine like terms.
2. ⓑ
  
  Multiply using the binomial square pattern.
  
  Simplify.
  
  Combine like terms.

Your turn

The book's Try It right after this example: same idea, new numbers. Only the answer is given.

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

How did it go?

PreviousMultiply Square Roots: example 9.55 Next Multiply Square Roots: example 9.57

From Elementary Algebra (1st edition) by OpenStax (Rice University), section 9.4, licensed under CC BY 4.0. Original at openstax.org. We split the solution into steps; the words, numbers and figures are the book's. OpenStax doesn't endorse this site.