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In $3-14,$ determine whether each of the numbers is rational or irrational.$$\frac{\sqrt{5}}{\sqrt{5}}$$

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Chapter 3

REAL NUMBERS AND RADICALS

Section 1

The Real Numbers and Absolute Value

Whole which of Numbers

Fractions and Mixed Numbers

Decimals

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In $3-14,$ determine wheth…

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02:25

01:49

01:38

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In $3-10,$ tell whether ea…

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our guys in this problem. We have the values square root by divided by square route five and we're being asked to determine if this value is an irrational number or a rational number. And the first step we're going to do is we're going to simplify the square. We're gonna simplify square root 50 divided by square root five. And what we're going to do first is we're going to rewrite it. So let's take a step back. Different color pen. So we have the square root of five, divided by the square root of five that is the same thing as a square root off. Five over five Justin Algebraic Step right here and the next up there were Hindus would do five, divided by 55 Divided by five is one, and we're taking the square root of one. And when you take the square root of 11 is a perfect square one. Basically, this is the same thing as square root of one squared the square root, and the square cancels out. So you're left with is just one and one by definition is a rational number. And since square with a five over five. Square 25 is equal to one. We know that this value right here this this whatever this value square defy over square 25 is a rational number. So let me recap that right. Really quickly. So the value that we found for when we simplified square root of five over square 25 is one which is a rational number. And since one is a rational number and one is equal to square 25 divided by scores of five, we can say that square with a five over Swear to five is a rational number. Okay, guys, I hope this help clarify some doubts because basically what we had to do was we just simplified whatever expression they gave us and determine if it was rational or irrational. And I hope this helps all the

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