How is the (2 x the Sqrt of 2) the same as Sqrt of 8

So how come 2 ( sqrt 2) is the same as the square root of 8?

How does it work, and what is the rule so I can apply to other questions to simplify square roots.

When simplifying square roots, you must find factors of the radicand (the expression under the radical) that are perfect squares...

√8 = √(4 * 2) = 2 √2

√32 = √(16 * 2) = 4 √2

√147 = √(49 * 3) = 7 √3

practice...read your textbook...practice some more.

So,
sqrt(8) = sqrt(4*2)=sqrt(4)*sqrt(2)=2*sqrt(2)

Pretty much, when something is in the square root, you can break it up into its factors which can be rooted easily.

ie. sqrt(63)=sqrt(9*7)=sqrt(9)*sqrt(7)=3*sqr…

good luck.

8 = 2 x 2 x 2

That means the largest perfect square that is a factor of 8 is 4. So sqrt(8) = sqrt(4 x 2) = sqrt(4) x sqrt(2) = 2 x sqrt(2)

√8= √2*4 =2√2


the square root of 4 is two so you then place two outside the square sign.

Sqrt(8) = Sqrt(4 x 2) = Sqrt(4) x Sqrt(2) = 2 x Sqrt(2) ---> That's how!!!

sqrt[8]= sqrt[2^3] =sqrt[2*2*2]=2Xsqrt[2]