Question

Using complete sentences, explain the two ways to simplify the square root of 180.and provide the simplified form.
You can show a square root by writing "sqrt()". For example, the square root of 2 can be written as "sqrt(2)".

Can someone explain a method i could slove this?

Answer 1

The best way to determine the square root of an integer is to first determine its prime factors. Thus
180 = 2 x 2 x 3 x 3 x 5
= 2^2 x 3^2 x 5
Hence sqrt(180) = sqrt(2^2 x 3^2 x 5)
= 2 x 3 x sqrt(5)
= 6*sqrt(5)
=
But wait a mo. A number x has two square roots;
So 180 -> +/- sqrt(180) = +/- 6*sqrt(5)
For me, that answer is complete as sqrt(5), being an irrational number cannot be accurately described in a fixed number of decimal of places.

However, if you wish to express the square root(s) of 180 to 3 decimal places say, then the solutions are
+/- sqrt(180)= +/- 13,416

Answer 2

is this good enough?

Answer 3

Oh Well that does seem to make sense.

Answer 4

Thank you for the explaination Sonya

Answer 5

No problem :)