Simplify by combing like terms 9 (sqaure root) 48 minus 4 (sqaure root) 27?

Question

Please show the steps.

Answer 1

Hi

It would help if you could put in the exact notation, but i think you mean this:

9√48 - 4√27

Listen up:

√48 = √(16x3) = √16 x √3 = 4 x √3 = 4√3

√27 = √(9x3) = √9 x √3 = 3 x √3 = 3√3

so putting this into the equation we get:

(9 x 4√3) - (4 x 3√3) = 36√3 - 12√3 = (36 - 12) x √3 = 24√3

Try to look hard at what ive done and youll see how it works.

Where the answer to a root, like √3, would give me a complicated decimal, ive left it as a root, but some can give exact values, like √16 = 4.

Also note: √48 = √16 x 3 = √16 x √3

48 is made of (16 x 3), so its equal, and the square root of two multiplied numbers is the same if you found the square root of each separately and multiplied them.

Another note: 36√3 - 12√3 = 24√3

If the number in the square root sign (here it is 3) is the same for both parts and you want to subtract or add them, just add/subtract the numbers before the root sign, and clump the result together as Ive done because 36 - 12 = 24


hope that helps :)

Answer 2

I open google.com I type in (9^48)-(4^27) you get 6.36268544 × 10^45