Westonci.ca is your go-to source for answers, with a community ready to provide accurate and timely information. Connect with a community of professionals ready to provide precise solutions to your questions quickly and accurately. Get immediate and reliable solutions to your questions from a community of experienced professionals on our platform.

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

Sagot :

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]

caylus

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]