Issolvi sqrt{6}left(3sqrt{2}+5sqrt{3}right)-7sqrt{48}

$$\sqrt{ 6 } \left( 3 \sqrt{ 2 } +5 \sqrt{ 3 } \right) -7 \sqrt{ 48 }$$

Evalwa

$$15\sqrt{2}-22\sqrt{3}\approx -16.891914331$$

Passi tas-Soluzzjonijiet

Uża l-propjetà distributtiva biex timmultiplika \sqrt{6} b'3\sqrt{2}+5\sqrt{3}.

$$3\sqrt{6}\sqrt{2}+5\sqrt{6}\sqrt{3}-7\sqrt{48}$$

Iffattura 6=2\times 3. Erġa' ikteb l-għerq kwadrat tal-prodott \sqrt{2\times 3} bħala l-prodott tal-għeruq kwadrati \sqrt{2}\sqrt{3}.

$$3\sqrt{2}\sqrt{3}\sqrt{2}+5\sqrt{6}\sqrt{3}-7\sqrt{48}$$

Immultiplika \sqrt{2} u \sqrt{2} biex tikseb 2.

$$3\times 2\sqrt{3}+5\sqrt{6}\sqrt{3}-7\sqrt{48}$$

Immultiplika 3 u 2 biex tikseb 6.

$$6\sqrt{3}+5\sqrt{6}\sqrt{3}-7\sqrt{48}$$

Iffattura 6=3\times 2. Erġa' ikteb l-għerq kwadrat tal-prodott \sqrt{3\times 2} bħala l-prodott tal-għeruq kwadrati \sqrt{3}\sqrt{2}.

$$6\sqrt{3}+5\sqrt{3}\sqrt{2}\sqrt{3}-7\sqrt{48}$$

Immultiplika \sqrt{3} u \sqrt{3} biex tikseb 3.

$$6\sqrt{3}+5\times 3\sqrt{2}-7\sqrt{48}$$

Immultiplika 5 u 3 biex tikseb 15.

$$6\sqrt{3}+15\sqrt{2}-7\sqrt{48}$$

Iffattura 48=4^{2}\times 3. Erġa' ikteb l-għerq kwadrat tal-prodott \sqrt{4^{2}\times 3} bħala l-prodott tal-għeruq kwadrati \sqrt{4^{2}}\sqrt{3}. Ħu l-għerq kwadrat ta' 4^{2}.

$$6\sqrt{3}+15\sqrt{2}-7\times 4\sqrt{3}$$

Immultiplika -7 u 4 biex tikseb -28.

$$6\sqrt{3}+15\sqrt{2}-28\sqrt{3}$$

Ikkombina 6\sqrt{3} u -28\sqrt{3} biex tikseb -22\sqrt{3}.

$$-22\sqrt{3}+15\sqrt{2}$$