# Root question, surds?

8√8 can be turned into m√2, where m is a positive integer.

Find m, and explain how you found it

Relevance
• Puggy
Lv 7

In order to reduce radicals (square roots), you have to decompose what's inside the square root.

sqrt(8) is the same as sqrt(4 * 2).

The square root of a product is the product of its square roots.

so sqrt(4 * 2) = sqrt(4) * sqrt(2)

We know what the square root of 4 is. It's 2.

sqrt(4)sqrt(2) = 2 sqrt(2).

In the above case, it's the exact same

8sqrt(8) = m sqrt(2)

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

8 sqrt(4)sqrt(2) = m sqrt(2)

8*2*sqrt(2) = m sqrt(2)

16 sqrt(2) = m sqrt(2)

Therefore, m = 16

• Luiz S
Lv 7

8√8 = m√2

8√(4*2) = m√2

8√4√2 = m√2

8*2√2 = m√2

16√2 = m√2

m = 16

• 1 decade ago

You find it by rewriting √8 as √(4 x √2, and replacing √4 with 2

So you have 8 x 2 √2 which is 16 √2

So m = 16

• 1 decade ago

Turn it into an equation:

8*sqrt(8) = m*sqrt(2)

divide both sides by sqrt(2):

8* sqrt(8)/sqrt(2) = m

m = 8 * sqrt(8/2)

m = 8 * sqrt (4)

m = 8 * 2

m=16