Question

whats the squareroot of 144 needs to be simplified

Answer 1

Answer:

12

Step-by-step explanation:

The square root of any number is basically asking "what number multiplied by itself will equal this number?"

Usually you memorize these, but there's also a quick way to do it.

We know that $10\cdot10=100$, so the square root must be greater than 10.

We also know that $15\cdot15=225$, so the square root must be less than 15.

A good mid point between these numbers is 13. Let's see what 13 squared is:

$13\cdot13=169$

So it's a bit less than 13. Let's try 12.

$12\cdot12=144$

So 12 is the square root of 144.

Hope this helped!

Answer 2

Answer:

$\huge\boxed{\sqrt{144}=12}$

Step-by-step explanation:

$\begin{array}{c|c}144&2\\72&2\\36&2\\18&2\\9&3\\3&3\\1\end{array}\\\\144=2\cdot2\cdot2\cdot2\cdot3\cdot3=2^2\cdot2^2\cdot3^2\\\\\sqrt{144}=\sqrt{2^2\cdot2^2\cdot3^2}=\sqrt{2^2}\cdot\sqrt{2^2}\cdot\sqrt{3^2}=2\cdot2\cdot3=12\\\\\text{Used}\\\\\sqrt{ab}=\sqrt{a}\cdot\sqrt{b}\\\sqrt{a^2}=a\\\\\text{for}\ a\ge0,\ b\geq0$