How do you simplify #3sqrt98-4sqrt28#?

Question

1698 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-06-25T21:41:17

See a solution process below:

First, rewrite the expression as:

#3sqrt(49 * 2) - 4sqrt(4 * 7)#

Next, use this rule for radicals to rewrite each radical:

#sqrt(color(red)(a) * color(blue)(b)) = sqrt(color(red)(a)) * sqrt(color(blue)(b))#

#3sqrt(color(red)(49) * color(blue)(2)) - 4sqrt(color(red)(4) * color(blue)(7)) =>#

#3sqrt(color(red)(49))sqrt(color(blue)(2)) - 4sqrt(color(red)(4))sqrt(color(blue)(7)) =>#

#(3 * 7)sqrt(color(blue)(2)) - (4 * 2))sqrt(color(blue)(7)) =>#

#21sqrt(2) - 8sqrt(7)#

Answer 2 · 2018-06-25T21:41:31

#21sqrt2-8sqrt7#

Let's see if we can factor a perfect square out of the radicals. The key here is that we can leverage the radical property

#sqrt(ab)=sqrtasqrtb#

We can rewrite #98# as #49*2# and #28# as #4*7#. We now have

#3sqrt(49*2)-4sqrt(4*7)#

#=>3*7sqrt2-4*2sqrt7#

We can simplify this to

#21sqrt2-8sqrt7#

Hope this helps!