## anonymous one year ago Simplify: √48

1. zzr0ck3r

$$\sqrt{48} = \sqrt{16*3}=\sqrt{16}\sqrt{3}=?$$

2. anonymous

4 and 3

3. zzr0ck3r

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

4. anonymous

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

5. mathstudent55

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: $$=4 \times \sqrt 3 = 4\sqrt 3$$