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Why are those numbers the same ?

15 Answers

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3√8=3√(4×2)

the 4 inside the radical sign can be taken outside by getting its square root, which is 2

3×2√2

6√2
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Thanks guys and girls :-)
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You could also factor it with fractional exponents which is good to know (just sqrt(8) part):

8^1/2 = 2^1/2 * 2^1/2 * 2^1/2
= 2^2/2 * 2^1/2
= 2 * 2^1/2

Rule:
a^1/n * a^1/n = a^(1/n + 1/n)
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off-topic but is this a good calculator? I just bought one the same model as yours.
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Sqrt8 can be broken down into sqrt4 x sqrt2 and since we know sqrt4=2 3x2 is 6 and sqrt2 is left we rewrite it as 6sqrt2. This is known as a simplified radical.
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Because the square root of 8 is exactly double the square root of 2.
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3  * sqrt 8 = sqrt 9 * sqrt 8 = sqrt 72

6 * sqrt 2 = sqrt 36 * sqrt 2 = sqrt 72

They both equal the square root of 72
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Move it all under the square root to see.
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3√8 = 3√4√2 =3(2)√2 = 6√2
Or
3√8 = √9√8 = √72 =√36√2 = 6√2
by
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3 * sqrt 8 = 3 * sqrt 2 * sqrt 4 = 3 * sqrt2 * 2 = 6sqrt2

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