Is the simplified form of 2 square root of 3 ⋅ 2 square root of 6 rational?

Mathematics

2 answers:

alina1380 [7]3 years ago

7 0

√3(√6)
= √3(6)
=√3(3·2)
=3√2

B. No the product will not be rational as 3√2 cannot be expressed as a simple fraction

Novosadov [1.4K]3 years ago

3 0

Yes it is
sry i had to type extra cuz it say "write at least 20 characters"
aghhh

You might be interested in

Ask your teacher find the limit. use l'hospital's rule where appropriate. if there is a more elementary method, consider using i

liberstina [14]

Answer:

ln(5/3)

Step-by-step explanation:

The desired limit represents the logarithm of an indeterminate form, so L'Hopital's rule could be applied. However, the logarithm can be simplified to a form that is not indeterminate.

<h3>Limit</h3>

We can cancel factors of (x-1), which are what make the expression indeterminate at x=1. Then the limit can be evaluated directly by substituting x=1.

$\diplaystyle \lim\limits_{x\to1}{(\ln(x^5-1)-\ln(x^3-1))}=\lim\limits_{x\to1}\ln{\left(\dfrac{x^5-1}{x^3-1}\right)}\\\\=\lim\limits_{x\to1}\ln\left(\dfrac{x^4+x^3+x^2+x+1}{x^2+x+1}\right)=\ln{\dfrac{5}{3}}$