Issolvi sqrt{15}(2sqrt{5}+sqrt{3})-2sqrt{75}=

$$\sqrt { 15 } ( 2 \sqrt { 5 } + \sqrt { 3 } ) - 2 \sqrt { 75 } =$$

Evalwa

$$3\sqrt{5}\approx 6.708203932$$

Passi tas-Soluzzjonijiet

Uża l-propjetà distributtiva biex timmultiplika \sqrt{15} b'2\sqrt{5}+\sqrt{3}.

$$2\sqrt{15}\sqrt{5}+\sqrt{15}\sqrt{3}-2\sqrt{75}$$

Iffattura 15=5\times 3. Erġa' ikteb l-għerq kwadrat tal-prodott \sqrt{5\times 3} bħala l-prodott tal-għeruq kwadrati \sqrt{5}\sqrt{3}.

$$2\sqrt{5}\sqrt{3}\sqrt{5}+\sqrt{15}\sqrt{3}-2\sqrt{75}$$

Immultiplika \sqrt{5} u \sqrt{5} biex tikseb 5.

$$2\times 5\sqrt{3}+\sqrt{15}\sqrt{3}-2\sqrt{75}$$

Immultiplika 2 u 5 biex tikseb 10.

$$10\sqrt{3}+\sqrt{15}\sqrt{3}-2\sqrt{75}$$

Iffattura 15=3\times 5. Erġa' ikteb l-għerq kwadrat tal-prodott \sqrt{3\times 5} bħala l-prodott tal-għeruq kwadrati \sqrt{3}\sqrt{5}.

$$10\sqrt{3}+\sqrt{3}\sqrt{5}\sqrt{3}-2\sqrt{75}$$

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

$$10\sqrt{3}+3\sqrt{5}-2\sqrt{75}$$

Iffattura 75=5^{2}\times 3. Erġa' ikteb l-għerq kwadrat tal-prodott \sqrt{5^{2}\times 3} bħala l-prodott tal-għeruq kwadrati \sqrt{5^{2}}\sqrt{3}. Ħu l-għerq kwadrat ta' 5^{2}.

$$10\sqrt{3}+3\sqrt{5}-2\times 5\sqrt{3}$$

Immultiplika -2 u 5 biex tikseb -10.

$$10\sqrt{3}+3\sqrt{5}-10\sqrt{3}$$

Ikkombina 10\sqrt{3} u -10\sqrt{3} biex tikseb 0.

$$3\sqrt{5}$$