Issolvi sqrt{9/2}+sqrt{25/8}+sqrt[3]{3000}-8sqrt[3]{3}-sqrt[3]{24}+sqrt{1/8}

$$\sqrt { \frac { 9 } { 2 } } + \sqrt { \frac { 25 } { 8 } } + \sqrt[ 3 ] { 3000 } - 8 \sqrt[ 3 ] { 3 } - \sqrt[ 3 ] { 24 } + \sqrt { \frac { 1 } { 8 } }$$

Evalwa

$$3\sqrt{2}\approx 4.242640687$$

Passi tas-Soluzzjonijiet

Erġa' ikteb id-diviżjoni tal-għerq kwadrat \sqrt{\frac{9}{2}} bħala d-diviżjoni tal-għeruq kwadrati \frac{\sqrt{9}}{\sqrt{2}}.

$$\frac{\sqrt{9}}{\sqrt{2}}+\sqrt{\frac{25}{8}}+\sqrt[3]{3000}-8\sqrt[3]{3}-\sqrt[3]{24}+\sqrt{\frac{1}{8}}$$

Ikkalkula l-għerq kwadrat ta' 9 u ikseb 3.

$$\frac{3}{\sqrt{2}}+\sqrt{\frac{25}{8}}+\sqrt[3]{3000}-8\sqrt[3]{3}-\sqrt[3]{24}+\sqrt{\frac{1}{8}}$$

Irrazzjonalizza d-denominatur tal-\frac{3}{\sqrt{2}} billi timmultiplika in-numeratur u d-denominatur mill-\sqrt{2}.

$$\frac{3\sqrt{2}}{\left(\sqrt{2}\right)^{2}}+\sqrt{\frac{25}{8}}+\sqrt[3]{3000}-8\sqrt[3]{3}-\sqrt[3]{24}+\sqrt{\frac{1}{8}}$$

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

$$\frac{3\sqrt{2}}{2}+\sqrt{\frac{25}{8}}+\sqrt[3]{3000}-8\sqrt[3]{3}-\sqrt[3]{24}+\sqrt{\frac{1}{8}}$$

Erġa' ikteb id-diviżjoni tal-għerq kwadrat \sqrt{\frac{25}{8}} bħala d-diviżjoni tal-għeruq kwadrati \frac{\sqrt{25}}{\sqrt{8}}.

$$\frac{3\sqrt{2}}{2}+\frac{\sqrt{25}}{\sqrt{8}}+\sqrt[3]{3000}-8\sqrt[3]{3}-\sqrt[3]{24}+\sqrt{\frac{1}{8}}$$

Ikkalkula l-għerq kwadrat ta' 25 u ikseb 5.

$$\frac{3\sqrt{2}}{2}+\frac{5}{\sqrt{8}}+\sqrt[3]{3000}-8\sqrt[3]{3}-\sqrt[3]{24}+\sqrt{\frac{1}{8}}$$

Iffattura 8=2^{2}\times 2. Erġa' ikteb l-għerq kwadrat tal-prodott \sqrt{2^{2}\times 2} bħala l-prodott tal-għeruq kwadrati \sqrt{2^{2}}\sqrt{2}. Ħu l-għerq kwadrat ta' 2^{2}.

$$\frac{3\sqrt{2}}{2}+\frac{5}{2\sqrt{2}}+\sqrt[3]{3000}-8\sqrt[3]{3}-\sqrt[3]{24}+\sqrt{\frac{1}{8}}$$

Irrazzjonalizza d-denominatur tal-\frac{5}{2\sqrt{2}} billi timmultiplika in-numeratur u d-denominatur mill-\sqrt{2}.

$$\frac{3\sqrt{2}}{2}+\frac{5\sqrt{2}}{2\left(\sqrt{2}\right)^{2}}+\sqrt[3]{3000}-8\sqrt[3]{3}-\sqrt[3]{24}+\sqrt{\frac{1}{8}}$$

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

$$\frac{3\sqrt{2}}{2}+\frac{5\sqrt{2}}{2\times 2}+\sqrt[3]{3000}-8\sqrt[3]{3}-\sqrt[3]{24}+\sqrt{\frac{1}{8}}$$

Immultiplika 2 u 2 biex tikseb 4.

$$\frac{3\sqrt{2}}{2}+\frac{5\sqrt{2}}{4}+\sqrt[3]{3000}-8\sqrt[3]{3}-\sqrt[3]{24}+\sqrt{\frac{1}{8}}$$

Ikkombina \frac{3\sqrt{2}}{2} u \frac{5\sqrt{2}}{4} biex tikseb \frac{11}{4}\sqrt{2}.

$$\frac{11}{4}\sqrt{2}+\sqrt[3]{3000}-8\sqrt[3]{3}-\sqrt[3]{24}+\sqrt{\frac{1}{8}}$$

Erġa' ikteb id-diviżjoni tal-għerq kwadrat \sqrt{\frac{1}{8}} bħala d-diviżjoni tal-għeruq kwadrati \frac{\sqrt{1}}{\sqrt{8}}.

$$\frac{11}{4}\sqrt{2}+\sqrt[3]{3000}-8\sqrt[3]{3}-\sqrt[3]{24}+\frac{\sqrt{1}}{\sqrt{8}}$$

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

$$\frac{11}{4}\sqrt{2}+\sqrt[3]{3000}-8\sqrt[3]{3}-\sqrt[3]{24}+\frac{1}{\sqrt{8}}$$

Iffattura 8=2^{2}\times 2. Erġa' ikteb l-għerq kwadrat tal-prodott \sqrt{2^{2}\times 2} bħala l-prodott tal-għeruq kwadrati \sqrt{2^{2}}\sqrt{2}. Ħu l-għerq kwadrat ta' 2^{2}.

$$\frac{11}{4}\sqrt{2}+\sqrt[3]{3000}-8\sqrt[3]{3}-\sqrt[3]{24}+\frac{1}{2\sqrt{2}}$$

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

$$\frac{11}{4}\sqrt{2}+\sqrt[3]{3000}-8\sqrt[3]{3}-\sqrt[3]{24}+\frac{\sqrt{2}}{2\left(\sqrt{2}\right)^{2}}$$

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

$$\frac{11}{4}\sqrt{2}+\sqrt[3]{3000}-8\sqrt[3]{3}-\sqrt[3]{24}+\frac{\sqrt{2}}{2\times 2}$$

Immultiplika 2 u 2 biex tikseb 4.

$$\frac{11}{4}\sqrt{2}+\sqrt[3]{3000}-8\sqrt[3]{3}-\sqrt[3]{24}+\frac{\sqrt{2}}{4}$$

Ikkombina \frac{11}{4}\sqrt{2} u \frac{\sqrt{2}}{4} biex tikseb 3\sqrt{2}.

$$3\sqrt{2}+\sqrt[3]{3000}-8\sqrt[3]{3}-\sqrt[3]{24}$$