How do you simplify #sqrt72 * sqrt32#?

2 Answers
Mar 2, 2018

The answer is #48#

Explanation:

To multiply square roots, it is easiest to just multiply the radicands (the numbers under the radical sign) and imagine the radical signs away for a minute.
So when we see:
#sqrt75 xx sqrt32# mentally remove the radicands and multiply.
#72 xx 32 = 2,304#

Now, we're going to put the radical sign back on and find the square root:
#sqrt2304 = 48#

Mar 2, 2018

# 48#

Explanation:

#sqrt72xxsqrt32#

#sqrt72=sqrt(2xx2xx2xx3xx3)#

#sqrt32=sqrt(2xx2xx2xx2xx2)#

Therefore,

#sqrt72xxsqrt32=sqrt(2xx2xx2xx3xx3)xxsqrt(2xx2xx2xx2xx2)#

#= 2xx3xxsqrt2xx2xx2xxsqrt2#

#= 2xx3xx2xx2xx2#

#= 48#

~Hope this helps! :)