Issolvi sqrt{(2*3^{2}-2^{2}*3)^{2}-4^{2}-(3^{5}:3^{4}+15^{2}:15^2)+2^5-5^5:5^4*7}

$$\sqrt { ( 2 \times 3 ^ { 2 } - 2 ^ { 2 } \times 3 ) ^ { 2 } - 4 ^ { 2 } - ( 3 ^ { 5 } : 3 ^ { 4 } + 15 ^ { 2 } : 15 ^ { 2 } ) + 2 ^ { 5 } - 5 ^ { 5 } : 5 ^ { 4 } \times 7 }$$

Evalwa

$$\sqrt{13}\approx 3.605551275$$

Passi tas-Soluzzjonijiet

Biex tiddividi l-qawwa tal-istess bażi, naqqas l-esponent tad-denominatur mill-esponent tan-numeratur. Naqas 4 minn 5 biex tikseb 1.

$$\sqrt{\left(2\times 3^{2}-2^{2}\times 3\right)^{2}-4^{2}-\left(3^{1}+\frac{15^{2}}{15^{2}}\right)+2^{5}-\frac{5^{5}}{5^{4}}\times 7}$$

Iddividi 15^{2} b'15^{2} biex tikseb1.

$$\sqrt{\left(2\times 3^{2}-2^{2}\times 3\right)^{2}-4^{2}-\left(3^{1}+1\right)+2^{5}-\frac{5^{5}}{5^{4}}\times 7}$$

Biex tiddividi l-qawwa tal-istess bażi, naqqas l-esponent tad-denominatur mill-esponent tan-numeratur. Naqas 4 minn 5 biex tikseb 1.

$$\sqrt{\left(2\times 3^{2}-2^{2}\times 3\right)^{2}-4^{2}-\left(3^{1}+1\right)+2^{5}-5^{1}\times 7}$$

Ikkalkula 3 bil-power ta' 2 u tikseb 9.

$$\sqrt{\left(2\times 9-2^{2}\times 3\right)^{2}-4^{2}-\left(3^{1}+1\right)+2^{5}-5^{1}\times 7}$$

Immultiplika 2 u 9 biex tikseb 18.

$$\sqrt{\left(18-2^{2}\times 3\right)^{2}-4^{2}-\left(3^{1}+1\right)+2^{5}-5^{1}\times 7}$$

Ikkalkula 2 bil-power ta' 2 u tikseb 4.

$$\sqrt{\left(18-4\times 3\right)^{2}-4^{2}-\left(3^{1}+1\right)+2^{5}-5^{1}\times 7}$$

Immultiplika 4 u 3 biex tikseb 12.

$$\sqrt{\left(18-12\right)^{2}-4^{2}-\left(3^{1}+1\right)+2^{5}-5^{1}\times 7}$$

Naqqas 12 minn 18 biex tikseb 6.

$$\sqrt{6^{2}-4^{2}-\left(3^{1}+1\right)+2^{5}-5^{1}\times 7}$$

Ikkalkula 6 bil-power ta' 2 u tikseb 36.

$$\sqrt{36-4^{2}-\left(3^{1}+1\right)+2^{5}-5^{1}\times 7}$$

Ikkalkula 4 bil-power ta' 2 u tikseb 16.

$$\sqrt{36-16-\left(3^{1}+1\right)+2^{5}-5^{1}\times 7}$$

Naqqas 16 minn 36 biex tikseb 20.

$$\sqrt{20-\left(3^{1}+1\right)+2^{5}-5^{1}\times 7}$$

Ikkalkula 3 bil-power ta' 1 u tikseb 3.

$$\sqrt{20-\left(3+1\right)+2^{5}-5^{1}\times 7}$$

Żid 3 u 1 biex tikseb 4.

$$\sqrt{20-4+2^{5}-5^{1}\times 7}$$

Naqqas 4 minn 20 biex tikseb 16.

$$\sqrt{16+2^{5}-5^{1}\times 7}$$

Ikkalkula 2 bil-power ta' 5 u tikseb 32.

$$\sqrt{16+32-5^{1}\times 7}$$

Żid 16 u 32 biex tikseb 48.

$$\sqrt{48-5^{1}\times 7}$$

Ikkalkula 5 bil-power ta' 1 u tikseb 5.

$$\sqrt{48-5\times 7}$$

Immultiplika 5 u 7 biex tikseb 35.

$$\sqrt{48-35}$$

Naqqas 35 minn 48 biex tikseb 13.

$$\sqrt{13}$$