Issolvi y=2(sqrt{360}+2sqrt{2}*sqrt{405})+3(sqrt{810}-sqrt{20}*sqrt{162})

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Linear Equation

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https://socratic.org/questions/given-the-sequence-a-1-sqrt-y-a-2-sqrt-y-sqrt-y-a-3-sqrt-y-sqrt-y-sqrt-y-cdots-d

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y=2\left(6\sqrt{10}+2\sqrt{2}\sqrt{405}\right)+3\left(\sqrt{810}-\sqrt{20}\sqrt{162}\right)

Iffattura 360=6^{2}\times 10. Erġa' ikteb l-għerq kwadrat tal-prodott \sqrt{6^{2}\times 10} bħala l-prodott tal-għeruq kwadrati \sqrt{6^{2}}\sqrt{10}. Ħu l-għerq kwadrat ta' 6^{2}.

y=2\left(6\sqrt{10}+2\sqrt{2}\times 9\sqrt{5}\right)+3\left(\sqrt{810}-\sqrt{20}\sqrt{162}\right)

Iffattura 405=9^{2}\times 5. Erġa' ikteb l-għerq kwadrat tal-prodott \sqrt{9^{2}\times 5} bħala l-prodott tal-għeruq kwadrati \sqrt{9^{2}}\sqrt{5}. Ħu l-għerq kwadrat ta' 9^{2}.

y=2\left(6\sqrt{10}+18\sqrt{2}\sqrt{5}\right)+3\left(\sqrt{810}-\sqrt{20}\sqrt{162}\right)

Immultiplika 2 u 9 biex tikseb 18.

y=2\left(6\sqrt{10}+18\sqrt{10}\right)+3\left(\sqrt{810}-\sqrt{20}\sqrt{162}\right)

Biex timmultiplika \sqrt{2} u \sqrt{5}, immultiplika n-numri taħt l-għerq kwadrat.

y=2\times 24\sqrt{10}+3\left(\sqrt{810}-\sqrt{20}\sqrt{162}\right)

Ikkombina 6\sqrt{10} u 18\sqrt{10} biex tikseb 24\sqrt{10}.

y=48\sqrt{10}+3\left(\sqrt{810}-\sqrt{20}\sqrt{162}\right)

Immultiplika 2 u 24 biex tikseb 48.

y=48\sqrt{10}+3\left(9\sqrt{10}-\sqrt{20}\sqrt{162}\right)

Iffattura 810=9^{2}\times 10. Erġa' ikteb l-għerq kwadrat tal-prodott \sqrt{9^{2}\times 10} bħala l-prodott tal-għeruq kwadrati \sqrt{9^{2}}\sqrt{10}. Ħu l-għerq kwadrat ta' 9^{2}.

y=48\sqrt{10}+3\left(9\sqrt{10}-2\sqrt{5}\sqrt{162}\right)

Iffattura 20=2^{2}\times 5. Erġa' ikteb l-għerq kwadrat tal-prodott \sqrt{2^{2}\times 5} bħala l-prodott tal-għeruq kwadrati \sqrt{2^{2}}\sqrt{5}. Ħu l-għerq kwadrat ta' 2^{2}.

y=48\sqrt{10}+3\left(9\sqrt{10}-2\sqrt{5}\times 9\sqrt{2}\right)

Iffattura 162=9^{2}\times 2. Erġa' ikteb l-għerq kwadrat tal-prodott \sqrt{9^{2}\times 2} bħala l-prodott tal-għeruq kwadrati \sqrt{9^{2}}\sqrt{2}. Ħu l-għerq kwadrat ta' 9^{2}.

y=48\sqrt{10}+3\left(9\sqrt{10}-18\sqrt{5}\sqrt{2}\right)

Immultiplika 2 u 9 biex tikseb 18.

y=48\sqrt{10}+3\left(9\sqrt{10}-18\sqrt{10}\right)

Biex timmultiplika \sqrt{5} u \sqrt{2}, immultiplika n-numri taħt l-għerq kwadrat.

y=48\sqrt{10}+3\left(-9\right)\sqrt{10}

Ikkombina 9\sqrt{10} u -18\sqrt{10} biex tikseb -9\sqrt{10}.

y=48\sqrt{10}-27\sqrt{10}

Immultiplika 3 u -9 biex tikseb -27.

y=21\sqrt{10}

Ikkombina 48\sqrt{10} u -27\sqrt{10} biex tikseb 21\sqrt{10}.