Question

which expression is equivalent to 4 square root 6 divided by 3 root 2

Answer 1

Answer:

The expression is equivalent to 4 square root 6 divided by 3 root 2 is:

8/3

Step-by-step explanation:

Given expression:

4 square root 6 divided by 3 root 2

$\frac{4\sqrt{6}}{3\sqrt{2} }$

$=\frac{4\sqrt{2*2*2}}{3\sqrt{2} }$

$=\frac{4\sqrt{2*2^{2} }}{3\sqrt{2} }$

square root of 2² = 2 hence,

$=\frac{4*2\sqrt{2}}{3\sqrt{2} }$

$=\frac{8\sqrt{2}}{3\sqrt{2} }$

Common terms in the numerator and denominator cancels each other out

$=\frac{8}{3}$

By solving the expression using simple mathematical rules, we got an equivalent expression of

$\frac{4\sqrt{6}}{3\sqrt{2} } = \frac{8}{3}$

Answer 2

Answer:

$\frac{4\sqrt{3} }{3}$

Step-by-step explanation:

Find a common factor between the numerator and the denominator, so that they may cancel out one another.

$\frac{4\sqrt{6} }{3\sqrt{2} } \\\\=\frac{4\sqrt{3*2} }{3\sqrt{2} } \\\\=\frac{4\sqrt{3}\sqrt{2}  }{3\sqrt{2} }$

Then by cancelling out the square root of 2:

$\frac{4\sqrt{3} }{3}$