How do you simplify #(sqrt9sqrt8)/(sqrt6sqrt6)?#

Question

Nathan Axel · Accepted Answer

#sqrt2# #(sqrt9sqrt8)/(sqrt6sqrt6)=(3*sqrt(2*4))/6# #=(3*2sqrt(2))/6=(6sqrt2)/6# #=sqrt2#

Ethan Adkins · Answer

There are different methods which can be used:

First option: Combine the radicals:

#(sqrt9sqrt8)/(sqrt6sqrt6) = sqrt72/sqrt36 = sqrt(72/36) = sqrt2#

Second option: Simplify where possible, find factors of radicands.

#(color(red)(sqrt9)color(blue)(sqrt8))/(color(green)(sqrt6sqrt6))#

#=(color(red)(3)color(blue)(sqrt(4xx2)))/(color(green)(sqrt6)^2)#

#=(color(red)(3)color(blue)(xx2sqrt(2)))/(color(green)(6)#

#=sqrt2#

Third option: Write as the product of prime factors:

#(sqrt9sqrt8)/(sqrt6sqrt6)#

#=(sqrt3 xx sqrt3 xxsqrt2xx sqrt2xx sqrt2)/(sqrt2xxsqrt3xxsqrt2xx sqrt3)" "# now cancel

#=(cancelsqrt3 xx cancelsqrt3 xxcancelsqrt2xx cancelsqrt2xx sqrt2)/(cancelsqrt2xxcancelsqrt3xxcancelsqrt2xx cancelsqrt3)#

#=sqrt2#

Savannah Anderson · Answer

undefined To simplify the expression (sqrt(9) * sqrt(8)) / (sqrt(6) * sqrt(6)), follow these steps:

1. Simplify each square root individually:
   - sqrt(9) = 3
   - sqrt(8) = 2 * sqrt(2)
   - sqrt(6) = sqrt(6)

2. Substitute the simplified values back into the expression:
   - (3 * 2 * sqrt(2)) / (sqrt(6) * sqrt(6))

3. Simplify further by canceling out the square roots of 6 in the denominator:
   - (3 * 2 * sqrt(2)) / (sqrt(6))^2
   - (3 * 2 * sqrt(2)) / 6

4. Divide both the numerator and the denominator by the common factor, 3:
   - (2 * sqrt(2)) / 2

5. Finally, simplify by canceling out the common factor of 2:
   - sqrt(2)