maths puzzles

[dougiemeats]

The resource book asks to simplify 3√5+2√6+√5. Now, would'nt the logical step be to subtract any surds of the same number in which would = 3√5+2√6?
The actual answer seems to be 4√5+2√6 but I have no idea why the integer four is there instead of what I initially thought of 3...

It's 4 because: 3√5 + √5 = 4√5

Think of it as: 3x + x = 4x

I hope that helps.

 

[wfooshee]

Meats has it: if you have 3 of something and then you have another one, how many somethings do you have? Don't make it harder just because of the square root signs. You're just adding up how many square-root-of-5's you have.

The subtraction you're wanting to do is for an equation with similar terms on both sides, like 3x+2y=x. You'd subtract an x from both sides to get 2x+2y=0. Doesn't change the value of anything. What you did changes the value, you just tossed part of the number away for no reason. "I have 3 apples and two oranges and another apple. That makes 4 apples and two oranges." It does NOT make 3 apples and 2 oranges.

 

[xXSilencerXx]

Got another query.

'Irrational' numbers are numbers that cannot be represented using a[FONT=&quot] ∕ b
whereas a and b are integers and b cannot be zero.

However, [FONT=&quot]√[/FONT]10 (3.16227766) is seen to be a 'irrational number' in my resource book where [FONT=&quot]√10 = 3.16227766.
But couldn't this number be multiplied by 100,000,000 (equaling 316,227,766) and therefore be applied as [/FONT][FONT=&quot]316,227,766[/FONT][FONT=&quot] ∕[/FONT][FONT=&quot]100,000,000. The result would be the original [/FONT]3.16227766, a & b are integers (which are whole numbers; no decimals if I am correct?) and b is not 0.

Therefore 3.16227766 would be rational no? Though I might be overlooking something here, I don't know...[/FONT]

The definition of an irrational number is a number that does not have a repeating or terminating decimal. It'll just keep going and going.