On questions such as the area is 3 times the square root of 2 + 5, how would you solve that algebraically?

Question

? My teacher has taught us two different methods to do so, such as foiling and square rooting it in the calculator, then square rooting it again, and square rooting each of the choices until it matches up. Please help!

Answer 1

Ambiguous as well. 

Is it 3(2)^(1/2) + 5,  OR  3(2 + 5)^(1/2)?

Not well presented.

 

Answer 2

When dealing with radicals (also known as square roots) the rule of the arithmetic standard process is the same for expressions within parentheses and radicals. I learned the process as:

"Please Excuse My Dear Aunt Sally"  to simplify expressions

"Parentheses, Exponents, Multiple, Divide, Add, Subtract"

The problem stated can be written as:

3 X √(2 + 5). Reading the expression from Left to Right,

1st Simplify expressions within Parentheses, in this case 2 + 5 = 7,

Our original expression is now : 3 X √7

As a teacher I accept 3√7 as the simplified answer. 

For the digital answer, now that we completed all Parentheses, will look from Left to Right for all Exponential expressions.

We know that √7 can also be stated as 7^(1/2); Solving we get 2.645751311.

Our original expression is now 3 X 2645751311, which when multiplied gives us:

The Answer =  7.93725933

Answer 3

We do not speculate or assume anything in mathematics.  You must be clear in what the problem is asking and what it is you need to find.  We can assume that its a circle, square, rectangle or a parallelogram, but we are not answering the questions.  Please resubmit with specifics.

Answer 4

Here's what you do.  They say the AREA is 3 times the square root of 2 + 5.  I am assuming by 2 + 5 you mean 7.  If the number 5 is NOT in the radical, then this whole thing would be 5 + 3sqrt(2) but I interpreted that as 3(sqrt(7)).

Now knowing that the area of this shape is 3sqrt(7) the way you figure out the other dimensions of the shape depends on what kind of shape it is.  If it's a circle, then you can solve for the radius and you will get (3(sqrt(7))/pi.  Then take the square root of THAT number and you have your exact radius to however accurately you want to round it.  God bless calculators.  The answer is about 1.59.  This is the radius of the circle.  Its diameter is about 3.18 and it's circumference is about 9.99.  You can figure all that out with a geometry cheat-sheet.

On the other hand, if it's a square you are looking for, then you just take the square root.  Don't worry about pi.  It's just the square root of 3sqrt(7).  It's about 2.82.  2.82 is the measurement (about) of each of the four sides of the square.  By the way, the perimeter of the square adds up to about 11.27.

If the shape is a rectangle, then you just take ANY pair of numbers you fancy and as long as they have a product of 3squrt(7), you're good.  You could start with 1 and 3sqrt(7) and of course, that's the area you get.  The perimeter of such a rectangle will vary but it will always be greater than 11.27.  I know this because that (11.27) is the perimeter of the square, and a square is the four-sided shape that MAXIMIZES area for a given perimeter length. 

Kudos and keep number crunchin'

Mr. Gets Results

Answer 5

Good morning, Sydney.

Did this problem tell you the shape for which the area is 3 rad 2 + 5?
For example, if the shape is a square, then you could let x = length of each side of the square.
Recall that Area of a square = side squared. 
So your equation would be:  x^2 = 3 rad 2 + 5

To solve using FOILing, you need to get every term to one side, so that you have an expression = zero:

x^2 - (3 rad 2 + 5) = 0  In this case I think FOILing may be a bit challenging.

To solve w/out FOIL, just square root both sides:

sqrt(x^2) = sqrt (3 rad 2 + 5)

x = sqrt (3 rad 2 + 5)

Carefully use your calculator to determine the answer.  
Hope this helped.