algebra

[timehi5]

how do you do problems like saquare root of 2(3 square root of 2 +square root of 5)
and (square root of 3- square root of 2)(5 square root of 2-4square root of 3)

 

[galactus]

Just distribute and use the laws of radicals. Such as \(\displaystyle \sqrt{a}\cdot \sqrt{a}=a\) and \(\displaystyle \sqrt{a}\cdot \sqrt{b}=\sqrt{ab}\)

\(\displaystyle \sqrt{2}(3\sqrt{2}+\sqrt{5})=3\sqrt{2}\cdot \sqrt{2}+\sqrt{5}\cdot \sqrt{2}=6+\sqrt{10}\)

 

[mmm4444bot]

For the second exercise, start by expanding the given expression using the FOIL algorithm (i.e., apply the Distributive Property twice).

(In math, the verb "to expand" means "to multiply".)

We use FOIL because the given expression is one binomial multiplied by another binomial. (Do you recognize this?)

Symbolically, the product of two binomials looks like:

(A + B)(C + D) = AC + AD + BC + BD

In your second exercise, the binomial factors are \(\displaystyle (\sqrt{3} - \sqrt{2})(5 \sqrt{2} - 4 \sqrt{3})\).

After you expand to find their product, simplify the resulting radicals (where possible), and finish by combining like-terms.

BTW, we can type square roots using the following convention.

[sqrt(3) - sqrt(2)]*[5 sqrt(2) - 4 sqrt(3)]

Please show whatever work that you can, if you would like more help with either of these exercises.

If you would like to learn more about how to properly type mathematical expressions, check out THIS SITE.

 

[timehi5]

thanks for telling me how to do this