What's the square root of x+5, and 5/x-6

square root of X+5 = [math]=\sqrt{X+5}[/math] and square root of 5/X - 6 = [math]\sqrt{\dfrac{5}{X} - 6}[/math]
Why was that hard for you?
 
Jomo said:
square root of X+5 = [math]=\sqrt{X+5}[/math] and square root of 5/X - 6 = [math]\sqrt{\dfrac{5}{X} - 6}[/math]
Why was that hard for you?
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Why not:

square root of X+5 = [math]=\sqrt{X}+5[/math]
 
Jomo said:
Because that would come from (square root of X) + 5
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Why not from:

square root of X+5 ............In PEMDAS we need Exponentiation before addition........... :ROFLMAO::ROFLMAO::ROFLMAO:
 
Jomo said:
It all depends on how you say it! If you say sqrt of x+5 or you say the sqrt of x ..... + 5 they are different.
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Sure ..... but you are not saying it - you are writing it!!
 
Jomo said:
I heard the OP saying it. You just have to listen. Turn on your speakers!
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Corner time is getting to you - you are seeing things, hearing things .... next you will start ghost story.............
 
CookieCat3 said:
What is the square root of X+5
What is the square root of 5/X-6
And what are the restrictions on X
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Hi CookieCat. While Jomo and Subhotosh play badminton, I will try to help you.

When you ask, "What is" the square root, are you asking how to type it?

Without knowing a value for X, we can't give a value for either square root.

I'm thinking the first one looks like √[X + 5]

In other words, the entire expression X+5 appears inside the radical sign. The square brackets show that. (We call the expression X+5 the 'radicand'.) If my guess for the radicand is not correct, then let us know.

The radical expression √[X + 5] represents a Real number that when multiplied by itself yields the number X+5. That's what the square root is.

The radical √[X + 5] cannot be simplifed (if that's what you meant to ask).

Here's a specific, numerical example, for a situation where we're told that X represents the number 11:

√[X + 5] = 4

Can you see why?

Your other question has to do with the domain of X. That is, the set of numbers for which √[X + 5] is defined in the Real number system.

You've probably been told that the radicand in a square root cannot be a negative number. (Again, the radicand is what we call the number or algebraic expression inside the square-root symbol.) This is important to remember: the value inside a square-root symbol cannot be negative, when we're working with Real numbers.

Example: √[-121] is not defined, in the Real number system.

Therefore, the expression X+5 cannot represent a negative number. What values do you think X can be?

I'll wait for you to finish the first one, before discussing the second radical. However, I will tell you about notation, when typing algebraic fractions.

I think the radicand in the second radical is supposed to be a ratio, with 5 in the numerator and X-6 in the denominator. (Let us know, if that's not correct.)

If so, then we need to type grouping symbols around the denominator, to clearly show what the denominator is supposed to be.

√[ 5/(X - 6) ]

The square brackets show that the entire expression 5/(X-6) is inside the square-root symbol. That is, they show us the radicand.

The parentheses show the denominator as X-6.

The situation is the same as with the first radical. The second radical cannot be simplified. We can't give a numerical value for it (without first knowing a value for X). All we know is that when multiplied by itself, the result will be the radicand:

√[ 5/(X - 6) ] times √[ 5/(X - 6) ] = 5/(X - 6)

Like before, you need to think about values for X that will cause the expression √[5/(X - 6)] to be undefined. The domain will consist of the remaining Real numbers. Those are the values for which the radical does evaluate to a Real number.

If you're uncertain about anything, then please ask specific questions. Thanks!

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