Math help!!!?

Question

Simplify!!

16a^2 (with a radical check mark sign over the problem)

72/8X^2 (with a radical check mark sign over the problem)

54w^16/150Z^4 (with a radical check mark sign over the problem)

I apologize...I dont know how to make that sign on the computer.

Thanks for your help!!!!

Answer 1

These square roots (radical check marks) are evaluated in the following way:

sqrt(16*a^2)
= sqrt(4^2*a^2)
= 4*a

The square root simply divides the exponent of the term inside it by 2. Four to the power of two (which is 16) becomes four to the power of one (which is just 4). a^2 becomes a.

However, it is NOT CORRECT to say that
sqrt(a^2 + 3^2) = a + 3

But it IS correct to say that
sqrt( (a + 3)^2 ) = a + 3

As long as there is no addition and subtraction going on inside the radical, simply take the square root of every term.

Answer 2

The basic principle used in these problems is this:

√(ab) = (√a)(√b)
also
(√a)(√b) = √(ab)

√(36r^2) = (√36)(√r^2) = 6 r

√(a/b) = (√a)/(√b)

√(48n^6/3m^4) = (√48/3)(√n^6)/(√m^4) = (√16)(n^3)/(m^2) = 4n^3/m^2

With fractions under the radical, you can divide (or reduce) them.

When you take the square root of something, you're dividing its exponent by two. √(a^12) = a^6; √(a^200) = a^100

If you wind up with a radical in the denominator, you need to multiply both the numerator and the denominator by a radical to get the radical in the denominator to be a perfect square so that the radical goes away.

1/(√2) = ((1) * (√2)) / ((√2) * (√2)) = (√2)/(√4) = (√2)/2

Usually you multiply by the same radical that's in the denominator, but you might not have to.

4
---
√8

You could multiply this by √2/√2 and still get a perfect square under the radical in the denominator.

(4)(√2)
----------
(√8)(√2)

equals

4√2
-----
√16

equals

4√2
------
4

equals

√2

Answer 3

the radical check mark sign means square root. it's the inverse of squared (^2). this should get you started.

Answer 4

1. 4a
2. 3/X
3. ((9 root 2) times w^8)) over ((5 root 6) times z^4))

P.S., if you have a graphing calculator, you can check these by plugging in values for a,x, etc...

Answer 5

Um, It is not our responsibility to do your math homework for you. Then you wouldnt learn anything. Use a calc? Use your head? Use your brain?

Answer 6

O_O
I'm still in special math. We're doing polygons! :D

Answer 7

1)4a
2)3/x
3)(3w^8)/(5z^2)
vote for me for best answer cause i helped you :)