Lahenda =32585-786*408/10/sqrt{[62280frac{786^2{10}][17412408^2/10]}}

$$= \frac { 32585 - \frac { 786 \times 408 } { 10 } } { \sqrt { [ 62280 \frac { 786 ^ { 2 } } { 10 } ] [ 17412 \frac { 408 ^ { 2 } } { 10 } ] } }$$

Arvuta

$$\frac{2581\sqrt{7530690}}{14490011488320}\approx 0,000000489$$

Lahenduse etapid

Korrutage 786 ja 408, et leida 320688.

$$\frac{32585-\frac{320688}{10}}{\sqrt{62280\times \frac{786^{2}}{10}\times 17412\times \frac{408^{2}}{10}}}$$

Taandage murd \frac{320688}{10} vähimale ühiskordsele, eraldades ja taandades arvu 2.

$$\frac{32585-\frac{160344}{5}}{\sqrt{62280\times \frac{786^{2}}{10}\times 17412\times \frac{408^{2}}{10}}}$$

Teisendage 32585 murdarvuks \frac{162925}{5}.

$$\frac{\frac{162925}{5}-\frac{160344}{5}}{\sqrt{62280\times \frac{786^{2}}{10}\times 17412\times \frac{408^{2}}{10}}}$$

Kuna murdudel \frac{162925}{5} ja \frac{160344}{5} on sama nimetaja, lahutage nende lugejad.

$$\frac{\frac{162925-160344}{5}}{\sqrt{62280\times \frac{786^{2}}{10}\times 17412\times \frac{408^{2}}{10}}}$$

Lahutage 160344 väärtusest 162925, et leida 2581.

$$\frac{\frac{2581}{5}}{\sqrt{62280\times \frac{786^{2}}{10}\times 17412\times \frac{408^{2}}{10}}}$$

Arvutage 2 aste 786 ja leidke 617796.

$$\frac{\frac{2581}{5}}{\sqrt{62280\times \frac{617796}{10}\times 17412\times \frac{408^{2}}{10}}}$$

Taandage murd \frac{617796}{10} vähimale ühiskordsele, eraldades ja taandades arvu 2.

$$\frac{\frac{2581}{5}}{\sqrt{62280\times \frac{308898}{5}\times 17412\times \frac{408^{2}}{10}}}$$

Avaldage 62280\times \frac{308898}{5} ühe murdarvuna.

$$\frac{\frac{2581}{5}}{\sqrt{\frac{62280\times 308898}{5}\times 17412\times \frac{408^{2}}{10}}}$$

Korrutage 62280 ja 308898, et leida 19238167440.

$$\frac{\frac{2581}{5}}{\sqrt{\frac{19238167440}{5}\times 17412\times \frac{408^{2}}{10}}}$$

Jagage 19238167440 väärtusega 5, et leida 3847633488.

$$\frac{\frac{2581}{5}}{\sqrt{3847633488\times 17412\times \frac{408^{2}}{10}}}$$

Korrutage 3847633488 ja 17412, et leida 66994994293056.

$$\frac{\frac{2581}{5}}{\sqrt{66994994293056\times \frac{408^{2}}{10}}}$$

Arvutage 2 aste 408 ja leidke 166464.

$$\frac{\frac{2581}{5}}{\sqrt{66994994293056\times \frac{166464}{10}}}$$

Taandage murd \frac{166464}{10} vähimale ühiskordsele, eraldades ja taandades arvu 2.

$$\frac{\frac{2581}{5}}{\sqrt{66994994293056\times \frac{83232}{5}}}$$

Avaldage 66994994293056\times \frac{83232}{5} ühe murdarvuna.

$$\frac{\frac{2581}{5}}{\sqrt{\frac{66994994293056\times 83232}{5}}}$$

Korrutage 66994994293056 ja 83232, et leida 5576127364999636992.

$$\frac{\frac{2581}{5}}{\sqrt{\frac{5576127364999636992}{5}}}$$

Kirjutage: allüksus \sqrt{\frac{5576127364999636992}{5}}: allüksus juured \frac{\sqrt{5576127364999636992}}{\sqrt{5}}.

$$\frac{\frac{2581}{5}}{\frac{\sqrt{5576127364999636992}}{\sqrt{5}}}$$

Tegurda 5576127364999636992=1924128^{2}\times 1506138. Kirjutage \sqrt{1924128^{2}\times 1506138} toote juured, kui see ruut \sqrt{1924128^{2}}\sqrt{1506138}. Leidke 1924128^{2} ruutjuur.

$$\frac{\frac{2581}{5}}{\frac{1924128\sqrt{1506138}}{\sqrt{5}}}$$

Ratsionaliseerige korrutades lugeja ja \sqrt{5} nimetaja \frac{1924128\sqrt{1506138}}{\sqrt{5}} nimetaja.

$$\frac{\frac{2581}{5}}{\frac{1924128\sqrt{1506138}\sqrt{5}}{\left(\sqrt{5}\right)^{2}}}$$

\sqrt{5} ruut on 5.

$$\frac{\frac{2581}{5}}{\frac{1924128\sqrt{1506138}\sqrt{5}}{5}}$$

\sqrt{1506138} ja \sqrt{5} korrutage numbrid, mis on sama juur.

$$\frac{\frac{2581}{5}}{\frac{1924128\sqrt{7530690}}{5}}$$

Jagage \frac{2581}{5} väärtusega \frac{1924128\sqrt{7530690}}{5}, korrutades \frac{2581}{5} väärtuse \frac{1924128\sqrt{7530690}}{5} pöördväärtusega.

$$\frac{2581\times 5}{5\times 1924128\sqrt{7530690}}$$

Taandage 5 nii lugejas kui ka nimetajas.

$$\frac{2581}{1924128\sqrt{7530690}}$$

Ratsionaliseerige korrutades lugeja ja \sqrt{7530690} nimetaja \frac{2581}{1924128\sqrt{7530690}} nimetaja.

$$\frac{2581\sqrt{7530690}}{1924128\left(\sqrt{7530690}\right)^{2}}$$

\sqrt{7530690} ruut on 7530690.

$$\frac{2581\sqrt{7530690}}{1924128\times 7530690}$$

Korrutage 1924128 ja 7530690, et leida 14490011488320.

$$\frac{2581\sqrt{7530690}}{14490011488320}$$