what is the diagonal of a square who's area is 36.?

Question

Im getting the square root of 72 but they are saying the answer is 6 x square root of 2. They show the work right down to the same answer I'm getting then they some how magicaly determine the square root of 72 = 6 x the square root of 2. How are they converting this please?

Answer 1

6

Answer 2

Its about 13. Look...if it's 36 and it's a square, then all the sides must be 9 units long. If you make a triangle with 9 unit legs, that gives you 9 and 9. If you use the Pythagorean theorem, you square the two and add them together to get the square of the hypotenuse. 81 + 81= 162. The square root of 162...is I don't know. Let me whip out my calculator....12.72. Since 13 * 13 is 169, you should be able to guess that it's near there. Its a good idea, when doing math, to make a rough estimate of what kind of answer you'll be getting so you know you're on the right track while doing the problem. Oh shizzle. I just made my own mistake. You said area. Not perimeter. Oh, well in that case it's 6 and 6 which would give you the square root of 72. OK here we go.

You have a square. The area is 36. That gives you 6*6, yes? The triangle's two legs (think of an L) are therefore also 6 and 6. The Pythagorean theorem states that squaring leg 1 and squaring leg 2 and adding them together will give you the square of the hypotenuse (Which is the diagonal in this case). So that gives you 36+36=72. 72 is the square of the diagonal. Find the square root of 72 and you have the length, which is 8.485. Now the whole square root of two thing is a way mathematicians simplify radicals. If you have the square root of 64, for example, you could say that 64=2*2*2*2*2*2, right? Well, since its under a radical, you take two of them out and you can put it so that 2 *(radical) 2*2*2*2*2=64 instead of 6 of them. Or you could make it 4* (radical) 2*2*2*2=64. Or you could make it 8 (Which, remember, is the same as 2*2*2) times 2*2*2=64. The square root of 2 is 1.41...ish. If you multiply 6*1.41 ish you get 8.485...ish. Hazah! The value we came up with. Basically, this is a way of writing an answer without having to use decimals or do math. Why is this done? Because the square root use is an exact answer. That's what the answer IS. When using 8.485 (ish, lol) its an approximation. Also, you don't have to do any math. So, for the square root of 72, simplified, you would make it 2*3*12, and continue to simplify until you ended up with 6 * (radical) 2.

Answer 3

Area is 36. Area is length x height. Since it is a square and not a rectangle, the sides are equal lengths, so to get the length of the sides you can take the square root of 36, which is six. Then, to get the length of the diagonal, use the pythagorean theory a squared + b squared = c squared, where c is your diagonal. So, 36 + 36 = 72. Your answer is the square root of 72. 72 doesn't have an exact square root, but the answer is about 8.45.

Anyways.. you got that far already. The answer is 6 x the square root of 2 because that is as much as you can simplify the square root of 72.

Answer 4

The answer is the square root of 72. 72 does equal six times the square root of 2. The square root of 72 can be expressed as the square root of 36 times the square root of 2. The square root of 36 is 6. The square root of 2 can't be expressed as a whole number. So, the square root of 72 can be simplified into 6 times the square root of 2.

Answer 5

A square has sides of equal length.

The area of a square is length * height, or length * length.

Let length of a side of this square be of length x.

x*x = 36
x^2 = 36
to find the length x, take the square root of 36, which is 6. The length of each side of the square is of length 6.

Now, draw a diagonal from one corner to the other corner of the square. A square has four right (90 degree) angles, so drawing the diagonal will make two equal right triangles, whose other angles are each 45 degrees.

A 45-45-90 right triangle is one of those special triangles whose proportions are easy to memorize. side = 1, side = 1, diagonal/hypotenuse = radical 2 = the square root of 2 = sqrt(2)

So, since the sides of your square (and therefore your right 45-45-90) triangle is 6, your diagonal/hypotenuse is 6*sqrt(2).


You could also solve using the Pythagorean theorem, a^2 + b^2 = c^2. In this case, a = b (sides are equal) and a = 6, so
2*(a^2) = c^2
2*(6^2) = c^2
take the square root of both sides
sqrt(2) * (sqrt(6^2) = c
sqrt(2) * 6 = c


So you know, to find the square root of 72: sqrt(72)
Find all the factors of 72:
sqrt(2*2*2*3*3)
is the same as sqrt(2) * sqrt(2) * sqrt(2) * sqrt(3) * sqrt(3)
the squareroot of a number times the squareroot of that same number is just that number.
sqrt(2) * 2 * 3
sqrt(2) * 6

Answer 6

If the area is 36 and it's a square then the sides are 6 each. Bisect from diagional and you get a right angled triangle. Usinmg Pythgoras

(6 X 6) +( 6 x 6) = 36 + 36 = 72
So Diagonal is square root of 72

(I haven't got a calculator so its around 8 1/4)

Answer 7

72 is 36 times 2. So another way to write the square root of 72 is the square root of 36 times the square root of 2. Since the square root of 36 is 6, you can write it as 6 times the square root of 2.

Answer 8

6 times the square root of two is the same thing as the square root of 72, it is just simplified.

Answer 9

its a special triangle
if you draw the diagonal, you get two identical triangles
they are isosceles as well

square root of 72 is equal to the square root of 36 x the square root of 2

which equals 6 x square root of 2

Answer 10

72 is 36 * 2 so the square root of 36 is 6 and u are left with the square of 2 so the answer is 6 on the square root of 2

Answer 11

the diagonal of a square with and area of 36 is 6. because you get area by multiplying 2 sides. which is 6 x 6. the diagonal of this will be six. draw it out.

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