Issolvi frac{6sqrt{12}+2sqrt{30}+15sqrt{18}-5sqrt{45}}{39}

$$\frac{ 6 \sqrt{ 12 } +2 \sqrt{ 30 } +15 \sqrt{ 18 } -5 \sqrt{ 45 } }{ 39 }$$

Evalwa

$$\frac{2\sqrt{30}}{39}+\frac{4\sqrt{3}}{13}+\frac{15\sqrt{2}}{13}-\frac{5\sqrt{5}}{13}\approx 1.585580807$$

Passi tas-Soluzzjonijiet

Iffattura 12=2^{2}\times 3. Erġa' ikteb l-għerq kwadrat tal-prodott \sqrt{2^{2}\times 3} bħala l-prodott tal-għeruq kwadrati \sqrt{2^{2}}\sqrt{3}. Ħu l-għerq kwadrat ta' 2^{2}.

$$\frac{6\times 2\sqrt{3}+2\sqrt{30}+15\sqrt{18}-5\sqrt{45}}{39}$$

Immultiplika 6 u 2 biex tikseb 12.

$$\frac{12\sqrt{3}+2\sqrt{30}+15\sqrt{18}-5\sqrt{45}}{39}$$

Iffattura 18=3^{2}\times 2. Erġa' ikteb l-għerq kwadrat tal-prodott \sqrt{3^{2}\times 2} bħala l-prodott tal-għeruq kwadrati \sqrt{3^{2}}\sqrt{2}. Ħu l-għerq kwadrat ta' 3^{2}.

$$\frac{12\sqrt{3}+2\sqrt{30}+15\times 3\sqrt{2}-5\sqrt{45}}{39}$$

Immultiplika 15 u 3 biex tikseb 45.

$$\frac{12\sqrt{3}+2\sqrt{30}+45\sqrt{2}-5\sqrt{45}}{39}$$

Iffattura 45=3^{2}\times 5. Erġa' ikteb l-għerq kwadrat tal-prodott \sqrt{3^{2}\times 5} bħala l-prodott tal-għeruq kwadrati \sqrt{3^{2}}\sqrt{5}. Ħu l-għerq kwadrat ta' 3^{2}.

$$\frac{12\sqrt{3}+2\sqrt{30}+45\sqrt{2}-5\times 3\sqrt{5}}{39}$$

Immultiplika -5 u 3 biex tikseb -15.

$$\frac{12\sqrt{3}+2\sqrt{30}+45\sqrt{2}-15\sqrt{5}}{39}$$