How do you multiply #\sqrt { 130} \cdot \sqrt { 26}#?

1 Answer
Anirudh E.
Sep 17, 2017

See below.

Explanation:

Whenever you multiply two square roots, you can simply do this:

#sqrt(130) * sqrt(26)#

#sqrt(130*26)#

This is a very useful tool, as you will find later on in mathematics. Anyway, let's simplify this further:

#sqrt(130*26)#

#sqrt(3380)#

This is not yet in simplest form, so we will have to factor the term under the #sqrt# in order to reach the final answer in simplest form. You may want to do the prime factorization of #3380# on paper first:

#sqrt(3380)#

#sqrt(2^2 * 5 * 13^2#

Now, we need to use the square root to remove the #2^2# and #13^2# from inside the radical:

#sqrt(2^2 * 5 * 13^2#

#(2*13)sqrt(5)#

#26sqrt(5)#

This is your final answer (#26sqrt(5)#), and it cannot be simplified any further.

I hope that helps!

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