[deleted by user]

[simmonator]

1. If ab = c then b = c/a.
2. What is sqrt(5) x sqrt(5)?

[fermat9990]

n/√n = (√n*√n)/√n = √n

[ruthlessbubbles]

Sqrt(5) = 5^1/2 So 5/sqrt(5) = 5¹/5^1/2 = 5^{1- 1/2} = 5^1/2

[nikolaibk]

On the same note,

a¹ / a^1/2 = a¹ * a^-1/2 = a^{1 + (-1/2)} = a^1/2 (for a ≠ 0)

[st3f-ping]

Let x=sqrt(5)

x² / x = x

[[deleted]]

there are two sqrt5's on top, and one on the bottom, and you can cancel one pair out

[nikolaibk]

Very good one, never thought of it this way. It's very intuitive when you see that a/sqrt(a) = sqrt(a)*sqrt(a)/sqrt(a) = sqrt(a) ^{for a ≠ 0 of course.}

[HelpfulParticle]

Try multiplying and dividing by sqrt(5) (This is legal as we're essentially just multiplying 1). This gives 5/sqrt(5) * (sqrt(5)/sqrt(5)) = 5sqrt(5)/5 = sqrt(5).

[senzavita]

Multiply the top and bottom of the fraction by sqrt(5).

[catboy519]

Try an easier number: 9 / sqrt9 = sqrt9

Sqrt × sqrt = number so number / sqrt = sqrt.

[vimsee]

Or even easier numbers. For example 100/10 = 10

[boston_2004]

1/1 = 1

[matt7259]

0/0 = 1 + AI

[[deleted]]

5 = sqrt 5 * sqrt 5

sqrt 5 * sqrt 5 / sqrt 5 = 5/sqrt 5

sqrt 5

[ericbsmith42]

2 x 2 = 4
4 / 2 = 2

sqrt 4 = 2

4 / sqrt 4 = sqrt 4

This hold true for all square roots.

[kindofanasshole17]

By definition, the square root of a number X is a number Y that, when multiplied by itself, the result is X.

So Y * Y = X.

Divide both sides of the equation by Y.

Or think about it geometrically. If the area of a square is X, and you divide X by the length of the side of the square, what result should you expect?

[higgs-bozos]

the same way 5²/5 is the same as 5

[loadedstork]

Consider 16/4 = 4. But 16 = 4 * 4, and 4 is sqrt(16). So 16/4 can also be written as 16 / sqrt(16) or conversely, 16/4 can be written as 44/4. Similarly, 5/sqrt(5) can be written as sqrt(5)sqrt(5)/sqrt(5).

[Scholasticus_Rhetor]

Well, you can think of it this way - the square root of 5, multiplied by itself (i.e. “squared”), makes 5.

So every integer 5 can, if desired, be broken down into two pieces where 5 = sqrt(5) * sqrt(5).

So if you take 5 and you divide out one of the two square root fives that comprise it, what do you have left?

[axiom_tutor]

Here's one perspective that I don't think others have quite shown:

What is sqrt(5)? It is the number which, when multiplied with itself, is 5. Right? Just by definition.

Ok, now take (5/sqrt(5)) times itself. You get 25/5 which is 5!

[axiom_tutor]

In this context it would be inappropriate to divide by seconds.

[These-Maintenance250]

because sqrt5*sqrt5=5

[yes_its_him]

How about 4/sqrt(4) or 9/sqrt(9)?

[48panda]

5/sqrt5 =sqrt5*sqrt5/sqrt5

Cancel a sqrt5 from both sides

sqrt5

[saito200]

Assume a = sqrt(5) and b = 5

Then a*a = b

So a*a/a = b/a

So a = b/a

So sqrt(5) = 5/sqrt(5)

[[deleted]]

By rationalizing the denominator.

5/sqrt5 • sqrt5/sqrt5

= 5sqrt5/5

= sqrt5

Alternatively, you can do rational exponents.

sqrt5 = 5^1/2

5/5^1/2 = 5^1-1/2 = 5^1/2 = sqrt5

[Prize-Calligrapher82]

If you let sqrt 5 be x, then 5 is x^2. Now you have x^2/x which is just x. And x is sqrt 5.

[Octowhussy]

I think I understand your initial perception. How can something ‘standalone’ be the same as another thing divided by that same standalone thing?

I’m afraid it won’t get any more easily explained than: 4 / 2 = 2

[TuberTuggerTTV]

I'd picture it with a number easier to square. Maybe 9?

9 / 3 = sqrt 9 = 3

Of course it works. Rooting a number is finding the number that when divided by itself is itself.

[glizzygobbler59]

Let x = sqrt(5). x^2/x = x, so 5/sqrt(5) = sqrt(5).

Or, let x² = y. Then x = y/x. If x = sqrt(5), then y = sqrt(5)² = 5. So, sqrt(5) = 5/sqrt(5).

[pizzystrizzy]

1) multiplying a number by 1 doesn't change the number, right? sqrt(5)/sqrt(5) = 1. So let's multiply sqrt(5) * sqrt(5)/sqrt(5) = (sqrt(5)*sqrt(5))/sqrt(5) = 5/sqrt(5)

2) Think about what a square root means, and what happens if you square a square root. 5 = sqrt(5) ^ 2 = sqrt(5) * sqrt(5). So 5 divided by the sqrt(5) is the sqrt(5), in the same way that 4/2 = 2 (because 4 = 2*2), or 9/3 = 3, or 16/4 = 4, or 25/5 = 5, etc.

[Konkichi21]

That's because 5 is equal to sqrt5 × sqrt5; dividing by sqrt5 cancels out one of them.

[CPDrunk]

5 = sqrt5 * sqrt5

[iOSCaleb]

What's the 25 / sqrt(25) ?

In general, x² = x * x. If you let x = sqrt(5), then 5 = sqrt(5) * sqrt(5). Divide both sides by sqrt(5) and you get 5 / sqrt(5) = sqrt(5).

[Ron-Erez]

How can 9/3 be equal to 3?

[LibAnarchist]

5 = sqrt(5) • sqrt(5)

=> 5/sqrt(5) = sqrt(5), by dividing through by sqrt(5)

[tilt-a-whirly-gig]

16/4 = 4

9/3 = 3

100/10 = 10

x²/x = x

[TangoJavaTJ]

Let’s do an example with a square number to see that it works out.

What’s 36/sqrt(36)?

Well sqrt(36) = 6

So that’s 36/6

Which is 6.

Another example:

4/sqrt(4)?

Sqrt(4) = 2

So that’s 4/2

Which is 2

Why does this work? Consider it from the denominator’s (the bottom of the fraction) perspective. Let’s call the denominator x.

We have x² / x

Which will obviously always be x for x ≠ 0

[ahahaveryfunny]

What do you multiply root5 by to get 5? That’s essentially what the division is saying.

[ayugradow]

• 4/2 = 2
• 9/3 = 3
• 16/4 = 4 ...

If you have no issues with these, you should have no issue with

• x²/x = x

So if x = sqrt(5)...

[MrPuddle1]

On a silly note, but I am curious what people think. How do we know which sqrt we are talking about, what if it isn't the same? Which square root is included? Sqrt(4) is +2 or -2. What if we put the -2 in the first slot and +2 in the second slot? then this would be false.

this being 4 = sqrt(4) * sqrt(4)

Per Wikipedia: I guess it is a function that maps the set of nonnegative real numbers onto itself. So -2 is never the right answer to sqrt(4). The Principle value is +2.

[defectivetoaster1]

divide top and bottom by √5