Question

Simplify: √48

Answer 1

\(\sqrt{48} = \sqrt{16*3}=\sqrt{16}\sqrt{3}=?\)

Answer 2

4 and 3

Answer 3

its just \(4\sqrt{3}\)

the square root of 16 is 4, but the square root of 3 is not so nice so we just write it as sqrt 3

Answer 4

oooh ok. thank you. i don't understand any of this

Answer 5

To simplify a root like this one, you need to find the greatest factor of 48 that is a perfect square.
Here are some whole numbers and their squares:
0 0
1 1
2 4
3 9
4 16
5 25
6 36
Look in the second column. They are the squares of the first 7 whole numbers.
One of them is the greatest factor of 48 that is a perfect square. It is 16.
Now you rewrite 48 as a product of the greatest perfect square factor and another factor:

\(\sqrt {48} = \sqrt { 16 \times 3} \)

Next you separate the roots. The product of two roots equals the root of the product.

\(= \sqrt{16} \times \sqrt 3\)

Finally, you take the square root of 16:

\(=4 \times \sqrt 3 = 4\sqrt 3\)