A level maths help (binomial question) Watch

Wisteria_xo
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#1
Report Thread starter 2 years ago
#1
Hey guys i'm stuck on this question (1 +√ x )^3
my method is
3C0 x (1)^3 x (√x)^0 = 1 x 1 x 1 = 1
3C1 x (1)^2 x (√x)^1 = 3 x 1 x √x = 3√x
3C2 x (1)^1 x (√x)^2 = 3 x 1 x x^2
3C3 x (1)^0 x (√x)^3 = 3 x 1 x √x . x^3

What I'm struggling to understand is why (√x)^2 is 2√x rather than x
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thefatone
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#2
Report 2 years ago
#2
(Original post by Wisteria_xo)
Hey guys i'm stuck on this question (1 +√ x )^3
my method is
3C0 x (1)^3 x (√x)^0 = 1 x 1 x 1 = 1
3C1 x (1)^2 x (√x)^1 = 3 x 1 x √x = 3√x
3C2 x (1)^1 x (√x)^2 = 3 x 1 x x^2
3C3 x (1)^0 x (√x)^3 = 3 x 1 x √x . x^3

What I'm struggling to understand is why (√x)^2 is 2√x rather than x
It's not \left(\sqrt x\right)^2=x

just like \left(\sqrt 2 \right)^2 = 2
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aadil10
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#3
Report 2 years ago
#3
(Original post by Wisteria_xo)
Hey guys i'm stuck on this question (1 +√ x )^3
my method is
3C0 x (1)^3 x (√x)^0 = 1 x 1 x 1 = 1
3C1 x (1)^2 x (√x)^1 = 3 x 1 x √x = 3√x
3C2 x (1)^1 x (√x)^2 = 3 x 1 x x^2
3C3 x (1)^0 x (√x)^3 = 3 x 1 x √x . x^3

What I'm struggling to understand is why (√x)^2 is 2√x rather than x
3rd line = 3 x 1 x X =3X
4th line = 3 x 1 x X^(3/2) = 3X^(3/2)
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thefatone
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#4
Report 2 years ago
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(Original post by aadil10)
3rd line = 3 x 1 x X =3X
4th line = 3 x 1 x X^(3/2) = 3X^(3/2)
I though that was wrong.. i was scared to say anything in case i got it wrong too ^-^

\sqrt x = x^{\frac{1}{2}}

\therefore \left(\sqrt x\right)^3= \left(x^{\frac{1}{2}}\right)^3= x^{\frac{3}{2}}
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