Issolvi frac{3sqrt{10}}{10}*frac{sqrt{5}}{5}+frac{sqrt{10}}{10}*frac{2sqrt{15}}{5}

$$\frac { 3 \sqrt { 10 } } { 10 } \times \frac { \sqrt { 5 } } { 5 } + \frac { \sqrt { 10 } } { 10 } \times \frac { 2 \sqrt { 15 } } { 5 }$$

Evalwa

$$\frac{\sqrt{2}\left(2\sqrt{3}+3\right)}{10}\approx 0.914162017$$

Passi Qosra tas-Soluzzjonijiet

Immultiplika \frac{3\sqrt{10}}{10} b'\frac{\sqrt{5}}{5} billi timmultiplika n-numeratur bin-numeratur u d-denominatur bid-denominatur.

$$\frac{3\sqrt{10}\sqrt{5}}{10\times 5}+\frac{\sqrt{10}}{10}\times \frac{2\sqrt{15}}{5}$$

Immultiplika \frac{\sqrt{10}}{10} b'\frac{2\sqrt{15}}{5} billi timmultiplika n-numeratur bin-numeratur u d-denominatur bid-denominatur.

$$\frac{3\sqrt{10}\sqrt{5}}{10\times 5}+\frac{\sqrt{10}\times 2\sqrt{15}}{10\times 5}$$

Annulla 2 fin-numeratur u d-denominatur.

$$\frac{3\sqrt{10}\sqrt{5}}{10\times 5}+\frac{\sqrt{10}\sqrt{15}}{5\times 5}$$

Biex iżżid jew tnaqqas l-espressjonijiet, espandihom biex id-denominaturi tagħhom ikunu l-istess. Espandi 5\times 5.

$$\frac{3\sqrt{10}\sqrt{5}}{5\times 10}+\frac{\sqrt{10}\sqrt{15}}{5\times 10}$$

Billi \frac{3\sqrt{10}\sqrt{5}}{5\times 10} u \frac{\sqrt{10}\sqrt{15}}{5\times 10} għandhom l-istess denominatur, żidhom billi żżid in-numeraturi tagħhom.

$$\frac{3\sqrt{10}\sqrt{5}+\sqrt{10}\sqrt{15}}{5\times 10}$$

Agħmel il-multiplikazzjonijiet fi 3\sqrt{10}\sqrt{5}+\sqrt{10}\sqrt{15}.

$$\frac{15\sqrt{2}+5\sqrt{6}}{5\times 10}$$

Espandi 5\times 10.

$$\frac{15\sqrt{2}+5\sqrt{6}}{50}$$

Fattur

$$\frac{\sqrt{2} {(\sqrt{2} \sqrt{6} + 3)}}{10} = 0.9141620172685642$$