Understand how to fix and simplify this radical expression

[@admnner21111]

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[@Kleermaker1000]

From 7:57 on and you see how it is done. :) Also possible: d^3/sqr. rt. d = d^3/d^1/2 = d^3 - 1/2 = d^2 1/2 = d^2 x d^1/2, which is the same as d^2 x sqr. rt. d. :)

[@johnnyragadoo2414]

Interesting food for thought. In this case, the simplest is d^2.5. In general, d^x/d^y = d^(x-y). Remember your slide rule. Division is subtraction of exponents. d^3/d^0.5 = d^(3-0.5). Now to check with a calculator and watch the video. Did I get it right?

[@johnnyragadoo2414]

Well, shucks. I thought this was going to show how simple use of logarithms doesn’t have to be a mystery. The base d log of d^3/sqrt(d) is 2.5.

[@oahuhawaii2141]

You almost looked like you were trying to do calculus, dy/dx.

[@johnnyflanker6553]

Beautiful example ! My answer is SQR of D^5th ! Basically the same !

[@oahuhawaii2141]

But your answer isn't in standard form, which is the objective of the problem.

[@DarekKoczwara]

@@oahuhawaii2141 Sqr is like exponent of 1/2. Therefore d^(5/2).

[@bobcornwell403]

I came up with d^2..5.

[@oahuhawaii2141]

What is "2..5"?

[@markjakeway2035]

@@oahuhawaii2141 Obviously a typo.

[@genelowry5666]

Yes, Simplified d^2(sqrt d)

[@agooddoctorfan651]

Yes easy 😎

[@oahuhawaii2141]

There's nothing "wrong" with the term. It just isn't in standard form: d³/√d = d^(3-1/2) = d^2.5, d ≠ 0 It's important to keep "d ≠ 0" in the final result because d = 0 isn't valid in the original term (divide by 0), so we must exclude it from the result.

[@markjakeway2035]

Indeed and it didn't need 'fixing'. I went straight to your answer, written as d^5/2.

[@nancysoutherlandmba5787]

Yes d^2 • sq root of d

[@DarekKoczwara]

I came up with d^2.5 Close enough.

[@climbeverest]

D=1

[@anthon3373]

Why couldnt i square both the numerator and denominator and so i would be left with d^5 even though this doesnt match the ans given by our teacher ...anybody...

[@warblerab2955]

You would be squaring the whole thing and that doesn't equal the original. For example:(1/3)^2 = 1/6, not 1/3. But 1/3 * 3/3 still = 1/3. (1/3 * 3/3 = 3/9 = 1/3)

[@anthon3373]

@@warblerab2955 thank you for that. appreciate u responding

[@oahuhawaii2141]

If you square the whole thing, you have to take the square root of the result to undo the effect. { FYI, I have only a few superscript characters, so I must change forms for the other powers. } √((d³/√d)²) = [(d^3/d^0.5)^2]^0.5 = [d^6/d^1]^0.5 = [d^5]^0.5 = d^2.5 Notes: α) He multiples by the numerator and denominator by √d, which has the net effect of multiplying by √d/√d or 1. This leaves the result unchanged, but puts the expression in a new form to aid in simplifying. β) Squaring an expression and then taking the square root is really taking the absolute value. That won't impact this problem, but you need to be aware of changing the result. For example, if you apply that to any negative value, then you alter its sign: √((-3)²) = √9 = 3 . In short, √(x²) = |x| . Ignoring this can be bad for other math problems. γ) He isn't being rigorous with his math. The original problem excludes d = 0 because we can't divide by 0. However, the simplified form of d²*√d doesn't exclude d = 0, so he's supposed to qualify his answer: d²*√d, d ≠ 0 . δ) The original problem excludes d < 0 when dealing with real numbers; we don't need to cite this restriction because the final result reflects the same restriction. When you work with complex numbers, d < 0 is allowed. BTW, d = 0 is still disallowed only because of the initial divide-by-0 issue, so we need to write d ≠ 0 .

[@fireantsarestrange]

All I saw was 3. I got this wrong.

[@suzannespence9636]

D to 5th power

[@oahuhawaii2141]

When you square an expression to simplify it, you need to take the square root to undo the effect of the square. Thus, the answer is the square root of d^5, which is d^(5/2) or d^2.5 . His d²*√d is the messier way of writing the answer. Notes: α) Squaring an expression and then taking the square root is really taking the absolute value. That won't impact this problem, but you need to be aware of changing the result. For example, if you apply that to any negative value, then you alter its sign: √((-3)²) = √9 = 3 . In short, √(x²) = |x| . Ignoring this can be bad for other math problems. β) He isn't being rigorous with his math. The original problem excludes d = 0 because we can't divide by 0. However, the simplified form of d²*√d doesn't exclude d = 0, so he's supposed to qualify his answer as: d²*√d, d ≠ 0 . γ) The original problem excludes d < 0 when dealing with real numbers; we don't need to cite this restriction because the final result reflects the same restriction. When you work with complex numbers, d < 0 is allowed. BTW, d = 0 is still disallowed only because of the initial divide-by-0 issue, so we need to write d ≠ 0 .

[@iceberg54321]

DxD? Are you an anime fan? Dungeons and Dragons?

[@jannielsen6784]

D

[@GiorgioSemprevivo]

First comment.😁