Ratkaise sqrt{6^4*81^25/243^20*16}

$$\sqrt { \frac { 6 ^ { 4 } \cdot 81 ^ { 25 } } { 243 ^ { 20 } \cdot 16 } }$$

Laske

$$9$$

Ratkaisun vaiheet

Laske 6 potenssiin 4, jolloin ratkaisuksi tulee 1296.

$$\sqrt{\frac{1296\times 81^{25}}{243^{20}\times 16}}$$

Laske 81 potenssiin 25, jolloin ratkaisuksi tulee 515377520732011331036461129765621272702107522001.

$$\sqrt{\frac{1296\times 515377520732011331036461129765621272702107522001}{243^{20}\times 16}}$$

Kerro 1296 ja 515377520732011331036461129765621272702107522001, niin saadaan 667929266868686685023253624176245169421931348513296.

$$\sqrt{\frac{667929266868686685023253624176245169421931348513296}{243^{20}\times 16}}$$

Laske 243 potenssiin 20, jolloin ratkaisuksi tulee 515377520732011331036461129765621272702107522001.

$$\sqrt{\frac{667929266868686685023253624176245169421931348513296}{515377520732011331036461129765621272702107522001\times 16}}$$

Kerro 515377520732011331036461129765621272702107522001 ja 16, niin saadaan 8246040331712181296583378076249940363233720352016.

$$\sqrt{\frac{667929266868686685023253624176245169421931348513296}{8246040331712181296583378076249940363233720352016}}$$

Jaa 667929266868686685023253624176245169421931348513296 luvulla 8246040331712181296583378076249940363233720352016, jolloin ratkaisuksi tulee 81.

$$\sqrt{81}$$

Laske luvun 81 neliöjuuri, saat vastaukseksi 9.

$$9$$

Jaa tekijöihin

$$3^{2}$$