Issolvi left(sqrt{3}+1right)left(sqrt{3}-2right)+sqrt{12}-{left(sqrt{3}+1right)}^0

$$\left( \sqrt{ 3 } +1 \right) \left( \sqrt{ 3 } -2 \right) + \sqrt{ 12 } - { \left( \sqrt{ 3 } +1 \right) }^{ 0 }$$

Evalwa

$$\sqrt{3}\approx 1.732050808$$

Passi tas-Soluzzjonijiet

Uża l-propjetà distributtiva biex timmultiplika \sqrt{3}+1 b'\sqrt{3}-2 u kkombina termini simili.

$$\left(\sqrt{3}\right)^{2}-\sqrt{3}-2+\sqrt{12}-\left(\sqrt{3}+1\right)^{0}$$

Il-kwadrat ta' \sqrt{3} huwa 3.

$$3-\sqrt{3}-2+\sqrt{12}-\left(\sqrt{3}+1\right)^{0}$$

Naqqas 2 minn 3 biex tikseb 1.

$$1-\sqrt{3}+\sqrt{12}-\left(\sqrt{3}+1\right)^{0}$$

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}.

$$1-\sqrt{3}+2\sqrt{3}-\left(\sqrt{3}+1\right)^{0}$$

Ikkombina -\sqrt{3} u 2\sqrt{3} biex tikseb \sqrt{3}.

$$1+\sqrt{3}-\left(\sqrt{3}+1\right)^{0}$$

Ikkalkula \sqrt{3}+1 bil-power ta' 0 u tikseb 1.

$$1+\sqrt{3}-1$$

Naqqas 1 minn 1 biex tikseb 0.

$$\sqrt{3}$$