Answered

IDNLearn.com is committed to providing high-quality answers to your questions. Join our community to receive timely and reliable responses to your questions from knowledgeable professionals.

(5√3-√27)^3
how do you prove that this is an integer?

Sagot :

Beinggreat78idn

Keys:

  • [tex]\left(a\cdot \:b\right)^n=a^nb^n[/tex]

Step-by-step explanation:

[tex]\left(5\sqrt{3}-\sqrt{27}\right)^3\\\5\sqrt{3}-\sqrt{27}^3=\left(2\sqrt{3}\right)^3\\= 2\sqrt{3}\\\left(2\sqrt{3}\right)^3=2^3\left(\sqrt{3}\right)^3\\=2^3\left(\sqrt{3}\right)^3\\2^3=8\\=8\left(\sqrt{3}\right)^3\\=8\cdot \:3\sqrt{3}\\8\cdot \:3=24\\=24\sqrt{3}[/tex]

Caylusidn

Answer:

It is not an integer.

Step-by-step explanation:

[tex](5\sqrt{3} -\sqrt{27} )^3\\\\=(\sqrt{3} *(5-3))^3\\\\=8*3*\sqrt{3} \\\\=24\sqrt{3} \\[/tex]

Thank you for contributing to our discussion. Don't forget to check back for new answers. Keep asking, answering, and sharing useful information. Find clear and concise answers at IDNLearn.com. Thanks for stopping by, and come back for more dependable solutions.