How do I simplify this?

Question

Problem a) On top it says 6(square root of five). On the bottom it says square root of two.

Problem b) square root of fifty-six times square root of eight

Answer 1

a) 6sqrt(5)/sqrt(2)

You cannot leave a square root in the denominator, so remember that sqrt(2) times itself will get rid of the square root.

So, take 6 sqrt(5)/sqrt (2) times sqrt(2)/sqrt(2).

The expression becomes:

6 sqrt(5) sqrt(2)
--------------------
2

6/2 is 3, and sqrt(5)*sqrt(2) is sqrt(10), so this is the simplified form:

3sqrt(10)

--

b) sqrt(56) * sqrt(8)

Notice that 56 is divisible by 4 (4*14=56)
Also notice that 8 is divisible by 4 (4*2=8)
So, write the expression as

sqrt(4*14) * sqrt (4*2)

so you get

2sqrt(14) * 2sqrt(2)
which is
4sqrt(14)*sqrt(2)

Combine the numbers under the radicals:

4sqrt(28)

Note now that 28 is divisible by 4.

4sqrt(4*7)
=4*2sqrt(7)
=8sqrt(7)

Answer 2

a)
6√5/√2
6√5*√2/2
3√10

b)
√56*√8=√7*√8*√8=8√7

Answer 3

To simply radicals as the denominator simply multiply that fraction by a form of 1 using that radical:

(6sqrt5)/sqrt2 -> (sqrt2)(6sqrt5)/(sqrt2)^2
= 6sqrt10/2 = 3sqrt10


To multiply radicals simply multiply the numbers underneath the radicals.

Answer 4

6(5)^.5/2^.5

You have to rationalise it

6*5^.5 2^.5
-------- *
2^.5 2^.5

= 6*5^.5*2^.5
-----------------
4
= 3*10^.5
-----------
2

56^.5 * 8^.5
= 448^.5

Answer 5

i dunno