How do you simplify #sqrt(1,440)#?

2 Answers
Mar 9, 2018

Answer:

#12sqrt10#

Explanation:

#"note that " 1440=144xx10" and 144 is a perfect square"#

#"using the "color(blue)"law of radicals"#

#•color(white)(x)sqrt(ab)=sqrtaxxsqrtb#

#rArrsqrt1440=sqrt(144xx10)#

#color(white)(xxxxxxx)=sqrt144xxsqrt10=12sqrt10#

Mar 9, 2018

Answer:

#12sqrt10#

Explanation:

When you are simplifying radicals, you need to find two numbers. Between those two numbers, one HAS to be a perfect square, or it does not simplify.

Here, we are given:

#sqrt1440#

We can see here that there is an easy and more noticeable factorization:

#sqrt144 * sqrt10#

Thankfully, #144# is perfect square, so #sqrt144# can be reduced to #12#. Since #10# does not divide evenly into any prefect squares, #sqrt10# will no simplify.

Therefore, are answer will be:

#12sqrt10#