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A level maths help (binomial question)

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
(edited 7 years ago)
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 (x)2=x\left(\sqrt x\right)^2=x

just like (2)2=2\left(\sqrt 2 \right)^2 = 2
Reply 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


3rd line = 3 x 1 x X =3X
4th line = 3 x 1 x X^(3/2) = 3X^(3/2)
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 ^-^

x=x12\sqrt x = x^{\frac{1}{2}}

(x)3=(x12)3=x32\therefore \left(\sqrt x\right)^3= \left(x^{\frac{1}{2}}\right)^3= x^{\frac{3}{2}}

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