How do you simplify #sqrt45 + 5sqrt20 + 9sqrt3 + sqrt75#?

Question

Benjamin Altschul · Accepted Answer

#sqrt45+5sqrt20+9sqrt3+sqrt75=13sqrt5+14sqrt3# #sqrt45+5sqrt20+9sqrt3+sqrt75# = #sqrt(ul(3xx3)xx5)+5sqrt(ul(2xx2)xx5)+9sqrt3+sqrt(ul(5xx5)xx3)# = #3sqrt5+5xx2xxsqrt5+9sqrt3+5sqrt3# = #3sqrt5+10sqrt5+9sqrt3+5sqrt3# = #13sqrt5+14sqrt3#

Everly Taylor · Answer

undefined To simplify the expression sqrt(45) + 5sqrt(20) + 9sqrt(3) + sqrt(75), you can first factor out any perfect squares under the square roots and simplify them, then combine like terms.

sqrt(45) = sqrt(9 * 5) = 3sqrt(5)
sqrt(20) = sqrt(4 * 5) = 2sqrt(5)
sqrt(75) = sqrt(25 * 3) = 5sqrt(3)

Now substitute these simplified expressions back into the original expression:

3sqrt(5) + 5 * 2sqrt(5) + 9sqrt(3) + 5sqrt(3)

= 3sqrt(5) + 10sqrt(5) + 9sqrt(3) + 5sqrt(3)

Now combine like terms:

= (3sqrt(5) + 10sqrt(5)) + (9sqrt(3) + 5sqrt(3))

= 13sqrt(5) + 14sqrt(3)

So, sqrt(45) + 5sqrt(20) + 9sqrt(3) + sqrt(75) simplifies to 13sqrt(5) + 14sqrt(3).

How do you simplify #sqrt45 + 5sqrt20 + 9sqrt3 + sqrt75#?