Question

the sum of $sqrt{3}$ and 7 is...
show your work here
rational
irrational
find the perimeter of the following rectangle. give your answer in simplest radical form.
draw
$5sqrt{3}$
$2sqrt{3}$

Explanation:

Step1: Recall rational and irrational number definitions

A rational number can be written as $\frac{p}{q}$ where $p,q\in\mathbb{Z}$ and $q
eq0$. $\sqrt{3}$ is irrational as it cannot be written in $\frac{p}{q}$ form. 7 is rational.

Step2: Analyze sum property

The sum of a rational number $a$ and an irrational number $b$ is irrational. Let $a = 7$ (rational) and $b=\sqrt{3}$ (irrational). So, $7+\sqrt{3}$ is irrational.

Step3: Calculate rectangle perimeter

The perimeter $P$ of a rectangle with length $l = 5\sqrt{3}$ and width $w=2\sqrt{3}$ is given by $P = 2(l + w)$.
Substitute values: $P=2(5\sqrt{3}+2\sqrt{3})$.

Step4: Simplify perimeter expression

Using the distributive property and combining like - terms: $P=2\times(5 + 2)\sqrt{3}=2\times7\sqrt{3}=14\sqrt{3}$.

Answer:

1. Irrational
2. $14\sqrt{3}$