How to solve this math problem?

Question

This is a review question for my Math test tomorrow...no idea how to do it.

Simplify:
5 \/2 (\/8 + 7 \/2 - 5 \/8)

\/ is a square root sign...not sure how else to do it.

So, really not sure how to "simplify" this...a step by step answer would be awesome. =)

Answer 1

5 \/2 (\/8 + 7 \/2 - 5 \/8)
5 \/2 (2\/2 + 7 \/2 - 2 \/2)
5 \/2 (2\/2 + 7 \/2 - 5*2 \/2)
5 \/2 (2\/2 + 7 \/2 - 10 \/2)
5 \/2 (7 \/2 - 8 \/2)
- 5 \/2 \/2)
-5 * 2 = 10

Answer 2

5 √2 (√8 + 7 √2 - 5 √8)
√8=2√2
5√2(2√2+7√2-10√2)
5√2(-√2)
-10

Answer 3

Start by combining like terms and then multiplying it out.

5√2(√8 + 7√2 - 5√8) = 5√2(7√2 - 4√8)
= 35√4 - 20√16 = 35*2 - 20*4
= 70 - 80 = -10

Answer 4

5 sqrt(2) ( sqrt(8) + 7 sqrt(2) - 5 sqrt(8) )

There are two basic approaches.

One of them is as follows.

Multiply through by the 5 sqrt (2).

5 sqrt (2) sqrt(8) + 5 * 7 * sqrt(2) * sqrt(2) - 5 * 5 * sqrt(2) * sqrt(8)

= 5 sqrt(16) + 5 * 7 * sqrt(4) - 25 * sqrt(16)

= 5 * 4 + 5 * 7 * 2 - 25 * 4

= 20 + 70 - 100

= -10

The other way, is to notice that sqrt(8) = sqrt(4 * 2)
= sqrt(4) * sqrt(2) = 2 sqrt(2)

5 sqrt(2) ( sqrt(8) + 7 sqrt(2) - 5 sqrt(8) )
= 5 sqrt(2) ( 2 sqrt(2) + 7 sqrt(2) - 5 * 2 sqrt(2)

= 5 sqrt(2) ( [ 2 + 7 - 10 ] sqrt(2)

= 5 sqrt(2) * (-1 ) * sqrt(2)

= - 5 sqrt(2) * sqrrt(2)
= -5 * 2
= -10

Answer 5

I like that, V for square root.
Anyhow the key is to know that V8 is the same as V(2*4) which is the same as 2V2. Once you glom onto that, it sort of falls apart for you. So, rewrite the V8 as 2V2 and multiply through by 5V2.

You should end up with 10(2) + 35(2) - 50(2) = -5(2) = -10

Answer 6

I use SQRT(8) to write "square root of 8".
I use * as a multiplication sign.

One trick is to reduce the value inside the root to the smallest possible number.

SQRT(8) = SQRT(4*2) = SQRT(4) * SQRT(2) = 2 * SQRT(2)

So that, in your problem, 5*SQRT(8) becomes 10* SQRT(2)

From there, all your root values are SQRT(2) which becomes a common factor inside the bracket.

Answer 7

5 V2 (V8 + 7 V2 - 5 V8) = 5 V2 (V8) + 5 V2(7 V2) - 5 V2(5 V8)
distribute

= 5 V16 + 35 V4 - 25 V16
multiply radicals in each term

= 5(4) + 35(2) - 25(4)
since the radicands are perfect
squares, simplify

= 20 + 70 - 100

= -10

Answer 8

alrite multiply everything outside da brackets with everything inside da brackets in da order as it appears.
so afta da first multipiclation u are left with 5V16 (v stands for square root) and da square root of 16= 4 do den u times da 5 by 4 which gives u 20. Remember anything inside da root is multiplied with numbers inside da root only not numbers outside of it. Foloowing on da next multiplcation u are left with 35V4 and da square root of 4 is =2 so u are left with 70. Furthermore ur third multipilcation = -25V16 and da square root of 16 is once again 4 so u multiply -25 with 4 which gives u -100. NOw u simplify this by doing 20+70-100 which gives u -10.

-10 is yr ansa to dat

Answer 9

5 \/2 (\/8 + 7 \/2 - 5 \/8)

5 \/2 (2\/2 + 7 \/2 - 10 \/2)

5 \/2 (-1\/2)

5 (-2)

-10

Answer 10

Understand what's going on with these two simple formulas becuase they are necessary to solve the problem without a calculator.
You can change the variables to whatever letters you want
Z(a+b+c)= Za+Zb+Zc (ie 8(2+6+11)=8x2+8x6+8x11)
JVa x KVb = JKVaxb (ie 5V9 x 7V4 = 35V36 = 210)
You'll end up with
5V16 + 35V4 - 25V16 Don't forget to subtract the last term like I did at first.
20+70-100=-10
Robert