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In $43-47,$ express each answer in simplest radical form.The lengths of the sides of a triangle are $\sqrt{75}$ inches, $\sqrt{27}$ inches, and $\sqrt{108}$ inches. What is the perimeter of the triangle?

The perimeter of the triangle is 14$\sqrt{3}$ inches.

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Chapter 3

REAL NUMBERS AND RADICALS

Section 4

Adding and Subtracting Radicals

Whole which of Numbers

Fractions and Mixed Numbers

Decimals

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So in this problem, we're told that the three sidelines for triangle are the square, the 75 the square, the 27 in the square root of 108. And we want to find the perimeter. Will remember to find the perimeter. We simply add up all the sidelines. So we need to add to square the 75 plus the square, the 27 plus the square root of 108. Okay, great. Now we just need to simplify. So let's start by simplifying each of our radicals. So you know, the permanent equals Well, we'll start with the square that 75 the perfect square 25 goes into it three times. So we'll rewrite this as to square the 25 Times Square. The three. Now for our second radical to square the 27 the perfect square nine goes into it three times. So we'll rewrite this as two square than nine times to square the three. And then lastly, we have the square root of 108. Well, the perfect square. Um, I got lost there for a second there. Ah, 36 goes into it three times, so we can rewrite this as to square the 36 times the square, the three. Now let's go ahead and simplify each of these. Well, the square the 25 is five. So we'll have five or three for a next term. The square of the nine is three. So we're left with three for three. And from the last term, the square of the 36 is six. So we have 633 All right, great. Now we have, like, two terms here because they all have the same radic. And so we just need to simplify by combining the coefficients well. Five plus three is eight in a plus. Six is 14. So the perimeter will be 18. Brew three now, remember, they leave us units so the units for our per mother will be inches. So our final answer is that the perimeter of this triangle will be 18 route three inches

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