Issolvi 1/sqrt{5+2}+1/3sqrt{8}

$$\frac{ 1 }{ \sqrt{ 5+2 } } + \frac{ 1 }{ 3 \sqrt{ 8 } }$$

Evalwa

$$\frac{\sqrt{7}\left(\sqrt{14}+12\right)}{84}\approx 0.495815603$$

Passi Qosra tas-Soluzzjonijiet

Żid 5 u 2 biex tikseb 7.

$$\frac{1}{\sqrt{7}}+\frac{1}{3\sqrt{8}}$$

Irrazzjonalizza d-denominatur tal-\frac{1}{\sqrt{7}} billi timmultiplika in-numeratur u d-denominatur mill-\sqrt{7}.

$$\frac{\sqrt{7}}{\left(\sqrt{7}\right)^{2}}+\frac{1}{3\sqrt{8}}$$

Il-kwadrat ta' \sqrt{7} huwa 7.

$$\frac{\sqrt{7}}{7}+\frac{1}{3\sqrt{8}}$$

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}.

$$\frac{\sqrt{7}}{7}+\frac{1}{3\times 2\sqrt{2}}$$

Immultiplika 3 u 2 biex tikseb 6.

$$\frac{\sqrt{7}}{7}+\frac{1}{6\sqrt{2}}$$

Irrazzjonalizza d-denominatur tal-\frac{1}{6\sqrt{2}} billi timmultiplika in-numeratur u d-denominatur mill-\sqrt{2}.

$$\frac{\sqrt{7}}{7}+\frac{\sqrt{2}}{6\left(\sqrt{2}\right)^{2}}$$

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

$$\frac{\sqrt{7}}{7}+\frac{\sqrt{2}}{6\times 2}$$

Immultiplika 6 u 2 biex tikseb 12.

$$\frac{\sqrt{7}}{7}+\frac{\sqrt{2}}{12}$$

Biex iżżid jew tnaqqas l-espressjonijiet, espandihom biex id-denominaturi tagħhom ikunu l-istess. L-inqas multiplu komuni ta' 7 u 12 huwa 84. Immultiplika \frac{\sqrt{7}}{7} b'\frac{12}{12}. Immultiplika \frac{\sqrt{2}}{12} b'\frac{7}{7}.

$$\frac{12\sqrt{7}}{84}+\frac{7\sqrt{2}}{84}$$

Billi \frac{12\sqrt{7}}{84} u \frac{7\sqrt{2}}{84} għandhom l-istess denominatur, żidhom billi żżid in-numeraturi tagħhom.

$$\frac{12\sqrt{7}+7\sqrt{2}}{84}$$

Fattur

$$\frac{\sqrt{7} {(\sqrt{2} \sqrt{7} + 12)}}{84} = 0.49581560320698514$$