Explain how square root equation woks...?

Question

How does 2√2 = √8

How do you get the answer?

Answer 1

Sqrt[8]=Sqrt[4x2]=
Sqrt[4]xSqrt[2]=
2xSqrt[2]=
2Sqrt[2]

Answer 2

for this discussion, I'll use sqrt for square-root and sq for square.

So, how does 2√2 = √8?

lets take it one step at a time.

Whats sq(2)?
2 * 2 = 4.. Meaning, sqrt(4) = 2.

Now in the problem above, if I move the 2 outside the sqrt to inside the sqrt, I would have to sq it first. So the above can be also represented as:

2 * sqrt(2) = sqrt(4) * sqrt(2)
[Since from above sqrt(4) = 2]

Now, sqrt(4) * sqrt(2) can be represented as sqrt(4 * 2) = sqrt(8).

Answer 3

8 = 4 x 2
and sqrt of 4 = 2
so the 2 goes out and the other 2 stays in
so: sqrt 8 = 2 sqrt 2

Answer 4

<=square root symbol

<8 can be symplified, you take the biggest perfect square root that goes into 8, 4, and multiply it by 2 to get 8
therefore <8=<4<2 you can symplify <4
therefore <8=2<2

hope that helps!!

Answer 5

√8 = √(2x2x2) = √2√2x2 = (√2 )(2) = 2 √2
`

Answer 6

square root equation works like this:

5 [insert symbol here] 25

5 x 5 = 25

there's more too.

Answer 7

sqrt[ a * b ] = sqrt [ a ] * sqrt [ b ]
sqrt [ 8 ] = sqrt [ 4 ] * sqrt [ 2 ]
= 2 * sqrt [ 2 ]

Going in reverse, 2 = sqrt [ 2 ^ 2 ] = sqrt [ 4 ]
2 * sqrt [ 2 ] = sqrt [ 4 ] * sqrt [ 2 ] = sqrt [ 8 ]

Answer 8

since (√x)*(√x) = x therefore
2 = (√2)*(√2)
therefoe 2√2 = (√2)*(√2)*√2
and since (√x)*(√y) =(√x*y)
=√(2*2*2)
=√8