Simplify-4-2-3-

Question Number 180776 by Acem last updated on 17/Nov/22

S i m p l i f y \sqrt{\frac{4}{\sqrt{2}} + 3}

Answered by BaliramKumar last updated on 17/Nov/22

\sqrt{\frac{4}{\sqrt{2}} + 3}

\sqrt{2 \sqrt{2} + 3}

\sqrt{{(\sqrt{2} + 1)}^{2}}

\sqrt{2} + 1 A n s w e r

Commented by Acem last updated on 17/Nov/22

G o o d!, T h a n k s

Answered by manxsol last updated on 17/Nov/22

\sqrt{\frac{4}{\sqrt{2}} + 3} = \sqrt{a} + \sqrt{b}

2 \sqrt{2} + 3 = a + b + 2 \sqrt{a b}

a + b = 3

a b = 2

t^{2} - 3 t + 2 = 0

(t - 2) (t - 1)

a = 2

b = 1

\sqrt{\frac{4}{\sqrt{2}} + 3} = 1 + \sqrt{2}

Commented by Acem last updated on 17/Nov/22

G o o d t o o!, T h a n k s

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