Issolvi sqrt{80}+5sqrt{1/2}-3sqrt{5}+1/5sqrt{125}

Evalwa

Passi Qosra tas-Soluzzjonijiet

Fattur

Kwizz

Arithmetic

5 problemi simili għal:

Problemi Simili mit-Tiftix tal-Web

https://math.stackexchange.com/questions/2327261/what-is-the-value-of-sqrt1-sqrt-frac12-sqrt-frac18-sqrt-frac1

https://socratic.org/questions/how-do-you-evaluate-frac-a-sqrt-a-1-a-sqrt-a-frac-a-sqrt-a-1-a-sqrt-a

https://math.stackexchange.com/questions/509840/use-induction-to-prove-that-1-frac-1-sqrt2-frac-1-sqrt3

https://math.stackexchange.com/questions/2959669/how-did-i-obtain-incorrect-results-for-p-b-leftarrow-c-and-p-c-leftarrow-b

Sehem

Ikkupjat fuq il-klibbord

4\sqrt{5}+5\sqrt{\frac{1}{2}}-3\sqrt{5}+\frac{1}{5}\sqrt{125}

Iffattura 80=4^{2}\times 5. Erġa' ikteb l-għerq kwadrat tal-prodott \sqrt{4^{2}\times 5} bħala l-prodott tal-għeruq kwadrati \sqrt{4^{2}}\sqrt{5}. Ħu l-għerq kwadrat ta' 4^{2}.

4\sqrt{5}+5\times \frac{\sqrt{1}}{\sqrt{2}}-3\sqrt{5}+\frac{1}{5}\sqrt{125}

Erġa' ikteb id-diviżjoni tal-għerq kwadrat \sqrt{\frac{1}{2}} bħala d-diviżjoni tal-għeruq kwadrati \frac{\sqrt{1}}{\sqrt{2}}.

4\sqrt{5}+5\times \frac{1}{\sqrt{2}}-3\sqrt{5}+\frac{1}{5}\sqrt{125}

Ikkalkula l-għerq kwadrat ta' 1 u ikseb 1.

4\sqrt{5}+5\times \frac{\sqrt{2}}{\left(\sqrt{2}\right)^{2}}-3\sqrt{5}+\frac{1}{5}\sqrt{125}

Irrazzjonalizza d-denominatur tal-\frac{1}{\sqrt{2}} billi timmultiplika in-numeratur u d-denominatur mill-\sqrt{2}.

4\sqrt{5}+5\times \frac{\sqrt{2}}{2}-3\sqrt{5}+\frac{1}{5}\sqrt{125}

Il-kwadrat ta' \sqrt{2} huwa 2.

4\sqrt{5}+\frac{5\sqrt{2}}{2}-3\sqrt{5}+\frac{1}{5}\sqrt{125}

Esprimi 5\times \frac{\sqrt{2}}{2} bħala frazzjoni waħda.

\sqrt{5}+\frac{5\sqrt{2}}{2}+\frac{1}{5}\sqrt{125}

Ikkombina 4\sqrt{5} u -3\sqrt{5} biex tikseb \sqrt{5}.

\sqrt{5}+\frac{5\sqrt{2}}{2}+\frac{1}{5}\times 5\sqrt{5}

Iffattura 125=5^{2}\times 5. Erġa' ikteb l-għerq kwadrat tal-prodott \sqrt{5^{2}\times 5} bħala l-prodott tal-għeruq kwadrati \sqrt{5^{2}}\sqrt{5}. Ħu l-għerq kwadrat ta' 5^{2}.

\sqrt{5}+\frac{5\sqrt{2}}{2}+\sqrt{5}

Annulla 5 u 5.

2\sqrt{5}+\frac{5\sqrt{2}}{2}

Ikkombina \sqrt{5} u \sqrt{5} biex tikseb 2\sqrt{5}.

\frac{2\times 2\sqrt{5}}{2}+\frac{5\sqrt{2}}{2}

Biex iżżid jew tnaqqas l-espressjonijiet, espandihom biex id-denominaturi tagħhom ikunu l-istess. Immultiplika 2\sqrt{5} b'\frac{2}{2}.

\frac{2\times 2\sqrt{5}+5\sqrt{2}}{2}

Billi \frac{2\times 2\sqrt{5}}{2} u \frac{5\sqrt{2}}{2} għandhom l-istess denominatur, żidhom billi żżid in-numeraturi tagħhom.

\frac{4\sqrt{5}+5\sqrt{2}}{2}

Agħmel il-multiplikazzjonijiet fi 2\times 2\sqrt{5}+5\sqrt{2}.