How do you simplify #sqrt8/(2sqrt7)#?

Question

Hazel Anglin · Accepted Answer

#sqrt14/7#

#sqrt8/(2sqrt7)#

#(sqrt(4 * 2))/(2sqrt7)#

#(sqrt4 * sqrt2)/(2sqrt7)#

#(2sqrt2)/(2sqrt7)#

Since both the numerator and denominator is multiplied by #2#, we can cancel #2#: #(color(red)(cancel(2))sqrt2)/(color(red)(cancel(2))sqrt7)#

And what's left is: #sqrt2/sqrt7#

If you need to simplify it further, you can rationalize the denominator by multiplying the whole expression by #sqrt7#: #sqrt2/(sqrt7) * sqrt7/sqrt7#

Which becomes: #sqrt14/7#

Hope this helps!

Genesis Allen · Answer

undefined To simplify the expression sqrt8/(2sqrt7), we can simplify the numerator and denominator separately.

First, let's simplify the numerator, sqrt8. Since 8 can be written as 4 * 2, we can rewrite sqrt8 as sqrt(4 * 2). Taking the square root of 4 gives us 2, so sqrt8 simplifies to 2sqrt2.

Next, let's simplify the denominator, 2sqrt7. There are no perfect square factors in 7, so we cannot simplify it further.

Now, we can rewrite the expression as (2sqrt2)/(2sqrt7). Since the numerator and denominator have a common factor of 2, we can cancel them out, leaving us with sqrt2/sqrt7.

Finally, we can rationalize the denominator by multiplying both the numerator and denominator by sqrt7. This gives us (sqrt2 * sqrt7)/(sqrt7 * sqrt7), which simplifies to sqrt(2 * 7)/7.

Therefore, the simplified form of sqrt8/(2sqrt7) is sqrt14/7.