simplify:
2sqrt50 - sqrt8
I am confused because of the 2 before the sqrt50
2 sqrt 50 = 2 sqrt (5*5*2) = 10 sqrt 2
sqrt 8 - sqrt (2*2*2) = 2 sqrt 2
10 sqrt 2 - 2 sqrt 2 =
is 8sqrt2 correct?
The 2 before the sqrt50 just means 2 times sqrt50
Since
sqrt50=5sqrt2
and
sqrt8=2sqrt2
2*5sqrt2-2sqrt2
=10sqrt2-2sqrt2
=8sqrt2
Yes, both right :)
To simplify the given expression, 2sqrt50 - sqrt8, we can start by simplifying the square roots individually.
First, let's simplify sqrt50:
To do this, we need to find the largest perfect square that is a factor of 50. In this case, 25 is the largest perfect square that divides 50 evenly. Therefore, we can rewrite sqrt50 as sqrt(25 * 2).
Next, we can split the square root using the product property of square roots, which states that sqrt(a * b) = sqrt(a) * sqrt(b). Applying this, we can rewrite sqrt(25 * 2) as sqrt(25) * sqrt(2), which simplifies to 5sqrt2.
So, sqrt50 simplifies to 5sqrt2.
Now let's simplify sqrt8:
Similar to before, we need to find the largest perfect square that is a factor of 8. In this case, 4 is the largest perfect square that divides 8 evenly. Thus, sqrt8 can be rewritten as sqrt(4 * 2).
Using the product property of square roots, we can further simplify sqrt(4 * 2) as sqrt(4) * sqrt(2), which simplifies to 2sqrt2.
Therefore, sqrt8 simplifies to 2sqrt2.
Now, substituting these simplified values back into the original expression, we have:
2sqrt50 - sqrt8 = 2(5sqrt2) - (2sqrt2)
When performing the subtraction, we notice that the terms have the same radical part (sqrt2), so we can combine them:
2(5sqrt2) - (2sqrt2) = 10sqrt2 - 2sqrt2
Simplifying further, we subtract the coefficients:
10sqrt2 - 2sqrt2 = 8sqrt2
The simplified form of the expression 2sqrt50 - sqrt8 is 8sqrt2.