MHB Multiplying Radicals: Where Is My Mistake?

  • Thread starter Thread starter Cuberoot1
  • Start date Start date
  • Tags Tags
    Radicals
Click For Summary
SUMMARY

The discussion centers on the multiplication of radicals, specifically the expression (7-sqrt3a)(7+sqrt3a). The correct approach utilizes the difference of squares formula, resulting in 49 - (sqrt3a)^2. The user initially misapplied the distributive property, leading to an incorrect expression of 49 + 3a - 14sqrt3a. The key takeaway is to apply the identity (a-b)(a+b) = a^2 - b^2 for accurate results in such problems.

PREREQUISITES
  • Understanding of basic algebraic identities, specifically the difference of squares.
  • Familiarity with radical expressions and their properties.
  • Proficiency in simplifying algebraic expressions.
  • Basic calculator skills for verifying results.
NEXT STEPS
  • Study the difference of squares identity in greater detail.
  • Practice multiplying and simplifying radical expressions.
  • Learn about common mistakes in algebraic manipulations.
  • Explore advanced algebraic techniques for handling polynomials and radicals.
USEFUL FOR

Students learning algebra, educators teaching radical expressions, and anyone seeking to improve their skills in simplifying algebraic expressions.

Cuberoot1
Messages
4
Reaction score
0
I did this problem on paper but my calculator doesn't agree with the result. Can somebody tell me where I'm going wrong and how to do it right?

(7-sqrt3a)(7+sqrt3a)
= (7-sqrt3a)7+(7-sqrt3a)sqrt3a
= (7•7-7sqrt3a)+(7sqrt3a-sqrt3asqrt3a)
= 49-7sqrt3a+7sqrt3a-3a
= 49+3a-14sqrt3a

Even before I used the calculator something looked wrong, but I can't figure out how to fix it.
 
Mathematics news on Phys.org
Cuberoot said:
I did this problem on paper but my calculator doesn't agree with the result. Can somebody tell me where I'm going wrong and how to do it right?

(7-sqrt3a)(7+sqrt3a)
= (7-sqrt3a)7+(7-sqrt3a)sqrt3a
= (7•7-7sqrt3a)+(7sqrt3a-sqrt3asqrt3a)
= 49-7sqrt3a+7sqrt3a-3a
= 49+3a-14sqrt3a

Even before I used the calculator something looked wrong, but I can't figure out how to fix it.

(Wave)

$$(7-\sqrt{3a})(7+\sqrt{3a})=7 \cdot 7+ 7 \sqrt{3a}-7 \sqrt{3a}-(\sqrt{3a})^2=49-(\sqrt{3}a)^2$$
In general, it is known that $(a-b)(a+b)=a^2-b^2$.
 

Similar threads

De-Nesting Radicals: Solving & Simplifying Solutions
  • · Replies 4 ·
Replies
4
Views
4K
MHB How to simplify radicals in the denominator?
  • · Replies 7 ·
Replies
7
Views
2K
MHB Problem I am stuck on, simplifying radicals in denominator again
  • · Replies 5 ·
Replies
5
Views
2K
MHB Is FOIL used to multiply radicals in sqrt{x - 3} • sqrt{x}?
  • · Replies 10 ·
Replies
10
Views
2K
MHB Finding Discontinuities: Multiply by Conjugate?
  • · Replies 4 ·
Replies
4
Views
2K
High School Plotting the Solar System's planets' distances logarithmically
  • · Replies 17 ·
Replies
17
Views
3K
MHB Finding Time for a Kicked Ball
  • · Replies 5 ·
Replies
5
Views
3K
Undergrad Problem calculating Li-7 neutron - induced nuclear reaction
  • · Replies 10 ·
Replies
10
Views
3K
What's my mistake in this problem in dynamics involving pulleys?
  • · Replies 35 ·
2
Replies
35
Views
4K
MHB Calculate ways to form a committee of 3 from 8, DIRECTLY WITHOUT ÷?
  • · Replies 1 ·
Replies
1
Views
2K