Question

anyone know how to explain this to me?
(√(24)) * (√(72))

Answer 1

\[\sqrt{24}\times \sqrt{72}=\sqrt{24\times 72}\] but now you are supposed to notice that \(72=24\times 3\) giving you
\[\sqrt{24^2\times 3}=24\sqrt{3}\]

Answer 2

if that was not obvious, and it probably was not, you can factor
\(24=2^3\times 3\) and \(72=2^3\times 3^2\) so \(24\times 72=2^6\times 3^3\)

Answer 3

then \(\sqrt{2^6\times 3^3}=\sqrt{2^6\times 3^2}\times \sqrt{3}=2^3\times 3\times \sqrt{3}\)

Answer 4

Remember that \((ab)^n = a^nb^n\), \((a^m)^n = a^{(m*n)}\), and that \(\sqrt x = x^{1/2}\). The first bit allows you to factor or multiply square roots together, the second lets you see that \(\sqrt{2^6} = (2^6)^{1/2} = 2^3\), and the last is just a reminder of the other way you can write a square root so that you can use the properties of exponents.

Answer 5

I wish i could help but i havent learned this yet:/

Answer 6

(√(24)) * (√(72))

Answer 7

satellite73 sorry lost my connection

Answer 8

So from my understanding square root of 24 is?

Answer 9

square root of 6 which is square root of 3x2?

Answer 10

\[\sqrt{24} = \sqrt{4*6} = \]

Answer 11

whpalmer4 ok

Answer 12

\[\sqrt{24} \times \sqrt{72} \]\[=\sqrt{24} \times \sqrt{3\times24} \]\[=\sqrt{24} \times \sqrt{3}\times\sqrt{24} \]\[=\sqrt{24}^2\times\sqrt{3}\]\[=24\sqrt{3} \]

Answer 13

square root of 4 is 2 right

Answer 14

Correct

Answer 15

ok so square root of 2 x 6 correct?

Answer 16

whpalmer4?

Answer 17

Yes, \(\sqrt{24} = \sqrt{4*6}= 2\sqrt{6}\)

Answer 18

whpalmer4 thank you

Answer 19

If you wanted to combine it with \(\sqrt{72}\),
\[\sqrt{24}*\sqrt{72} = 2\sqrt{6}*\sqrt{3*24} = 2\sqrt{6}*\sqrt{3}*2\sqrt{6} = 4*6*\sqrt{3} = 24\sqrt{3}\]
Same result, different route :-)

Answer 20

@whpalmer4 let me check that hold on

Answer 21

@whpalmer4 so what i the sq root of 24 again step by step?

Answer 22

@whpalmer4 ok I got it! thanks