Question

Whats the squareroot of 144 needs to be simplified

Answer 1

`\huge\boxed{√(144)=12}`

Explanation:

`\begin{array}c144&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\\\\√(144)=√(2^2\cdot2^2\cdot3^2)=√(2^2)\cdot√(2^2)\cdot√(3^2)=2\cdot2\cdot3=12\\\\\text{Used}\\\\√(ab)=√(a)\cdot√(b)\\√(a^2)=a\\\\\text{for}\ a\ge0,\ b\geq0`

Answer 2

12

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!