Solving Radical Equations: Multiplying and Simplifying Roots

In summary, to multiply (square root of 3 + square root of 5)(square root of 3-square root of6), you can use the FOIL method to get the following simplified expression: 3 - 3√6 + 3√5 - 5√2. However, this may not be the most accurate answer as it uses surds, a way to more accurately solve this problem would be to use rationalizing the denominator.
  • #1
Stratosphere
373
0

Homework Statement



(square root of 3 + square root of 5)(square root of 3-square root of6)

Homework Equations





The Attempt at a Solution


Im confused on what to multiply what with.
 
Physics news on Phys.org
  • #2


How would you multiply (x + y)(x - z) out?

The Bob
 
  • #3


I don't know but that's what I've gotten :
[tex] (\sqrt{3}+\sqrt{5})(\sqrt{3}-\sqrt{6})=\sqrt{3}(\sqrt{3}-\sqrt{6})+\sqrt{5}(\sqrt{3}-\sqrt{6})=\\
\sqrt{3}\cdot\sqrt{3}-\sqrt{3}\cdot\sqrt{6}+\sqrt{5}\cdot\sqrt{3}-\sqrt{5}\cdot\sqrt{6}=\\
=-2.846882916[/tex]
 
  • #4


Well that is a way to do it but you've not produced an 'accurate' answer by using surds. As this has been posted, Stratosphere what would you have done?

The Bob
 

1. What are radicals?

Radicals, also known as roots, are mathematical symbols used to indicate the inverse operation of raising a number to a certain power. They are represented by the radical sign (√) and are used to find the number that, when multiplied by itself a certain number of times, will result in the original number.

2. How do I simplify radicals?

To simplify radicals, you need to find the factors of the number inside the radical sign. Then, you can take out any factors that are perfect squares and write them outside the radical sign. The remaining factors can be left inside the radical sign.

3. What is the difference between a radical and an exponent?

A radical and an exponent are inverse operations. An exponent indicates how many times a number is multiplied by itself, while a radical tells you the number that was multiplied to get a certain number. For example, 32 = 9, while √9 = 3.

4. How do I add or subtract radicals?

To add or subtract radicals, the radicals must have the same radicand (number inside the radical sign). If they do, you can simply combine the coefficients (numbers outside the radical sign) and keep the radicand the same. If they do not have the same radicand, you can use the distributive property to simplify the expression.

5. Can radicals be negative?

Yes, radicals can be negative. However, they must follow certain rules for simplification. For example, the square root of a negative number is not a real number, so it is typically written as "i√" where i is the imaginary unit. Additionally, when adding or subtracting radicals, make sure to combine like terms and simplify further if possible.

Similar threads

  • Precalculus Mathematics Homework Help
Replies
8
Views
776
  • Precalculus Mathematics Homework Help
Replies
3
Views
818
  • Precalculus Mathematics Homework Help
Replies
6
Views
592
  • Precalculus Mathematics Homework Help
Replies
9
Views
2K
  • Precalculus Mathematics Homework Help
Replies
3
Views
997
  • Precalculus Mathematics Homework Help
Replies
12
Views
2K
  • Precalculus Mathematics Homework Help
Replies
12
Views
483
  • Precalculus Mathematics Homework Help
Replies
3
Views
1K
  • Precalculus Mathematics Homework Help
Replies
16
Views
2K
  • Precalculus Mathematics Homework Help
Replies
3
Views
1K
Back
Top