Question Number 49464 by Pk1167156@gmail.com last updated on 07/Dec/18
$$\mathrm{If}\:\:\mathrm{9}\sqrt{{x}}=\sqrt{\mathrm{12}}+\sqrt{\mathrm{147}},\:\mathrm{then}\:\mathrm{the}\:\mathrm{value} \\ $$$$\mathrm{of}\:{x}\:\mathrm{is} \\ $$
Commented by tanmay.chaudhury50@gmail.com last updated on 07/Dec/18
$${pls}\:{activate}\:{your}\:{mind}\:{by}\:{trying}\:{to}\:{solve}\:{problems} \\ $$$${by}\:{yourself}...{later}\:{post}\:{in}\:{forum}\:{if}\:{results}\:{not} \\ $$$${obtained}... \\ $$
Commented by afachri last updated on 07/Dec/18
$$\mathrm{what}\:\mathrm{a}\:\mathrm{comment}\:\mathrm{dude},\:\mathrm{motivating}\:\mathrm{one} \\ $$$$ \\ $$
Answered by tanmay.chaudhury50@gmail.com last updated on 07/Dec/18
$$\sqrt{\mathrm{12}}\:=\mathrm{2}\sqrt{\mathrm{3}}\:\:\:\:\sqrt{\mathrm{147}}\:=\mathrm{7}\sqrt{\mathrm{3}}\: \\ $$$$\mathrm{9}\sqrt{{x}}\:=\mathrm{2}\sqrt{\mathrm{3}}\:+\mathrm{7}\sqrt{\mathrm{3}}\:=\mathrm{9}\sqrt{\mathrm{3}}\: \\ $$$${x}=\mathrm{3} \\ $$
Answered by Kunal12588 last updated on 07/Dec/18
$${squaring}\:{both}\:{side} \\ $$$$\mathrm{81}{x}=\mathrm{12}+\mathrm{147}+\mathrm{2}×\mathrm{2}\sqrt{\mathrm{3}}×\mathrm{7}\sqrt{\mathrm{3}} \\ $$$$\mathrm{81}{x}=\mathrm{159}+\mathrm{84} \\ $$$${x}=\mathrm{243}/\mathrm{81}=\mathrm{3} \\ $$