<h2>Steps:</h2>
So before we jump into these problems, we must keep this particular rule in mind:
- Product Rule of Radicals: √ab = √a × √b. Additionally, remember that √a × √a = a
<h3>9.</h3>
So remember that the perimeter is the sum of all the sides. In this case:
So firstly, using the product rule of radicals we need to simplify these radicals as such:
Now, combine like terms (since they all have the same like term √3, they can all be added up):
<u>Your final answer is 17√3 in.</u>
<h3>10a.</h3>
For this, we will be using the pythagorean theorem, which is , where a and b are the legs of the right triangle and c is the hypotenuse of the triangle. In this case, √18 and √32 are our legs and we need to find the hypotenuse. Set up our equation as such:
From here we can solve for the hypotenuse. Firstly, solve the exponents (remember that square roots and squared power cancel each other out):
Next, add up the left side:
Lastly, square root both sides of the equation:
<u>The hypotenuse is √50 cm.</u>
<h3>10b.</h3>
Now, the process is similar to that of 9 so I will just show the steps to the final answer.
<u>The perimeter is 12√2 in.</u>
<h3>11.</h3>
Now, the process is still similar to question 9 but remember that this time we are working with <em>cube roots</em>.
Note that when adding the numbers together, 3 isn't a like term to the other 2 terms because it doesn't have ∛3 multiplied with it.
<u>The perimeter is 3 + 12∛3 in.</u>