Could someone help me with this please and thank you!! Will mark and star!!

Mathematics

1 answer:

timurjin [86]3 years ago

8 0

The rule for expressing a radical as a rational exponent is as follows:
$\sqrt[n]{x^y} = x^ \frac{y}{n}$
So, to find $\sqrt[3]{27x^2y^3z^4}$ use that rule.
The cube root of 27 is 3, so the equation will start with 3.
$3x^ \frac{2}{3} yz^ \frac{4}{3}$
Hope that helps!

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8_murik_8 [283]

A rational number is any number that can be written as the ratio between two other numbers i.e. in the form $\frac{a}{b}$

Part A:
An easy choice that makes sense is 7.8, right in the middle. To prove that it's rational we need to write it as a ratio. In this case we have $7.8=\frac{78}{10}$

Part B:
We need a number that can't be written as a ratio (because it neither terminates nor repeats). Some common ones are $\sqrt{2}$ , $e$ , $\phi$ and $\pi$ so it makes sense to try and use those to build our number. In this case $\frac{11\sqrt{2}}{5}\approx7.78$ works nicely.