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Simplify-4-2-3-




Question Number 180776 by Acem last updated on 17/Nov/22
Simplify  (√((4/( (√2))) + 3))
$${Simplify}\:\:\sqrt{\frac{\mathrm{4}}{\:\sqrt{\mathrm{2}}}\:+\:\mathrm{3}}\: \\ $$$$ \\ $$
Answered by BaliramKumar last updated on 17/Nov/22
(√((4/( (√2))) + 3 ))  (√(2(√(2 )) + 3 ))  (√(((√2) + 1)^2  ))  (√2) + 1 Answer
$$\sqrt{\frac{\mathrm{4}}{\:\sqrt{\mathrm{2}}}\:+\:\mathrm{3}\:} \\ $$$$\sqrt{\mathrm{2}\sqrt{\mathrm{2}\:}\:+\:\mathrm{3}\:} \\ $$$$\sqrt{\left(\sqrt{\mathrm{2}}\:+\:\mathrm{1}\right)^{\mathrm{2}} \:} \\ $$$$\sqrt{\mathrm{2}}\:+\:\mathrm{1}\:{Answer} \\ $$
Commented by Acem last updated on 17/Nov/22
Good! , Thanks
$${Good}!\:,\:{Thanks} \\ $$
Answered by manxsol last updated on 17/Nov/22
  (√((4/( (√2)))+3))=(√a)+(√b)  2(√2)+3=a+b+2(√(ab))  a+b=3  ab=2  t^2 −3t+2=0  (t−2)(t−1)  a=2  b=1  (√((4/( (√2)))+3))= 1+(√2)
$$ \\ $$$$\sqrt{\frac{\mathrm{4}}{\:\sqrt{\mathrm{2}}}+\mathrm{3}}=\sqrt{{a}}+\sqrt{{b}} \\ $$$$\mathrm{2}\sqrt{\mathrm{2}}+\mathrm{3}={a}+{b}+\mathrm{2}\sqrt{{ab}} \\ $$$${a}+{b}=\mathrm{3} \\ $$$${ab}=\mathrm{2} \\ $$$${t}^{\mathrm{2}} −\mathrm{3}{t}+\mathrm{2}=\mathrm{0} \\ $$$$\left({t}−\mathrm{2}\right)\left({t}−\mathrm{1}\right) \\ $$$${a}=\mathrm{2} \\ $$$${b}=\mathrm{1} \\ $$$$\sqrt{\frac{\mathrm{4}}{\:\sqrt{\mathrm{2}}}+\mathrm{3}}=\:\mathrm{1}+\sqrt{\mathrm{2}} \\ $$
Commented by Acem last updated on 17/Nov/22
Good too!, Thanks
$${Good}\:{too}!,\:{Thanks} \\ $$

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