Issolvi (2sqrt{8}-3sqrt{3}+5sqrt{32})-(3sqrt{27}-6sqrt{24})

$$( 2 \sqrt { 8 } - 3 \sqrt { 3 } + 5 \sqrt { 32 } ) - ( 3 \sqrt { 27 } - 6 \sqrt { 24 } )$$

Evalwa

$$12\left(\sqrt{6}+2\sqrt{2}-\sqrt{3}\right)\approx 42.55039272$$

Passi tas-Soluzzjonijiet

Iffattura 8=2^{2}\times 2. Erġa' ikteb l-għerq kwadrat tal-prodott \sqrt{2^{2}\times 2} bħala l-prodott tal-għeruq kwadrati \sqrt{2^{2}}\sqrt{2}. Ħu l-għerq kwadrat ta' 2^{2}.

$$2\times 2\sqrt{2}-3\sqrt{3}+5\sqrt{32}-\left(3\sqrt{27}-6\sqrt{24}\right)$$

Immultiplika 2 u 2 biex tikseb 4.

$$4\sqrt{2}-3\sqrt{3}+5\sqrt{32}-\left(3\sqrt{27}-6\sqrt{24}\right)$$

Iffattura 32=4^{2}\times 2. Erġa' ikteb l-għerq kwadrat tal-prodott \sqrt{4^{2}\times 2} bħala l-prodott tal-għeruq kwadrati \sqrt{4^{2}}\sqrt{2}. Ħu l-għerq kwadrat ta' 4^{2}.

$$4\sqrt{2}-3\sqrt{3}+5\times 4\sqrt{2}-\left(3\sqrt{27}-6\sqrt{24}\right)$$

Immultiplika 5 u 4 biex tikseb 20.

$$4\sqrt{2}-3\sqrt{3}+20\sqrt{2}-\left(3\sqrt{27}-6\sqrt{24}\right)$$

Ikkombina 4\sqrt{2} u 20\sqrt{2} biex tikseb 24\sqrt{2}.

$$24\sqrt{2}-3\sqrt{3}-\left(3\sqrt{27}-6\sqrt{24}\right)$$

Iffattura 27=3^{2}\times 3. Erġa' ikteb l-għerq kwadrat tal-prodott \sqrt{3^{2}\times 3} bħala l-prodott tal-għeruq kwadrati \sqrt{3^{2}}\sqrt{3}. Ħu l-għerq kwadrat ta' 3^{2}.

$$24\sqrt{2}-3\sqrt{3}-\left(3\times 3\sqrt{3}-6\sqrt{24}\right)$$

Immultiplika 3 u 3 biex tikseb 9.

$$24\sqrt{2}-3\sqrt{3}-\left(9\sqrt{3}-6\sqrt{24}\right)$$

Iffattura 24=2^{2}\times 6. Erġa' ikteb l-għerq kwadrat tal-prodott \sqrt{2^{2}\times 6} bħala l-prodott tal-għeruq kwadrati \sqrt{2^{2}}\sqrt{6}. Ħu l-għerq kwadrat ta' 2^{2}.

$$24\sqrt{2}-3\sqrt{3}-\left(9\sqrt{3}-6\times 2\sqrt{6}\right)$$

Immultiplika -6 u 2 biex tikseb -12.

$$24\sqrt{2}-3\sqrt{3}-\left(9\sqrt{3}-12\sqrt{6}\right)$$

Biex issib l-oppost ta' 9\sqrt{3}-12\sqrt{6}, sib l-oppost ta' kull terminu.

$$24\sqrt{2}-3\sqrt{3}-9\sqrt{3}-\left(-12\sqrt{6}\right)$$

Ikkombina -3\sqrt{3} u -9\sqrt{3} biex tikseb -12\sqrt{3}.

$$24\sqrt{2}-12\sqrt{3}-\left(-12\sqrt{6}\right)$$

L-oppost ta' -12\sqrt{6} huwa 12\sqrt{6}.

$$24\sqrt{2}-12\sqrt{3}+12\sqrt{6}$$