Ratkaise sqrt{frac{1+408*1610^-19/2*16710^-27left(310^8right)^2}2*167{10}^-27{left(3{10}^8right)}^2}{2}

$$\frac{ \sqrt{ \frac{ 1+408 \cdot 16 { 10 }^{ -19 } }{ 2 \cdot 167 { 10 }^{ -27 } { \left(3 { 10 }^{ 8 } \right) }^{ 2 } } } 2 \cdot 167 { 10 }^{ -27 } { \left(3 { 10 }^{ 8 } \right) }^{ 2 } }{ 2 }$$

Laske

$$\frac{3\sqrt{13046875000000008517}}{125000000000000}\approx 0,000086689$$

Ratkaisun vaiheet

Supista 2 ja 2.

$$167\sqrt{\frac{1+408\times 16\times 10^{-19}}{2\times 167\times 10^{-27}\times \left(3\times 10^{8}\right)^{2}}}\times 10^{-27}\times \left(3\times 10^{8}\right)^{2}$$

Kerro 408 ja 16, niin saadaan 6528.

$$167\sqrt{\frac{1+6528\times 10^{-19}}{2\times 167\times 10^{-27}\times \left(3\times 10^{8}\right)^{2}}}\times 10^{-27}\times \left(3\times 10^{8}\right)^{2}$$

Laske 10 potenssiin -19, jolloin ratkaisuksi tulee \frac{1}{10000000000000000000}.

$$167\sqrt{\frac{1+6528\times \frac{1}{10000000000000000000}}{2\times 167\times 10^{-27}\times \left(3\times 10^{8}\right)^{2}}}\times 10^{-27}\times \left(3\times 10^{8}\right)^{2}$$

Kerro 6528 ja \frac{1}{10000000000000000000}, niin saadaan \frac{51}{78125000000000000}.

$$167\sqrt{\frac{1+\frac{51}{78125000000000000}}{2\times 167\times 10^{-27}\times \left(3\times 10^{8}\right)^{2}}}\times 10^{-27}\times \left(3\times 10^{8}\right)^{2}$$

Selvitä \frac{78125000000000051}{78125000000000000} laskemalla yhteen 1 ja \frac{51}{78125000000000000}.

$$167\sqrt{\frac{\frac{78125000000000051}{78125000000000000}}{2\times 167\times 10^{-27}\times \left(3\times 10^{8}\right)^{2}}}\times 10^{-27}\times \left(3\times 10^{8}\right)^{2}$$

Kerro 2 ja 167, niin saadaan 334.

$$167\sqrt{\frac{\frac{78125000000000051}{78125000000000000}}{334\times 10^{-27}\times \left(3\times 10^{8}\right)^{2}}}\times 10^{-27}\times \left(3\times 10^{8}\right)^{2}$$

Laske 10 potenssiin -27, jolloin ratkaisuksi tulee \frac{1}{1000000000000000000000000000}.

$$167\sqrt{\frac{\frac{78125000000000051}{78125000000000000}}{334\times \frac{1}{1000000000000000000000000000}\times \left(3\times 10^{8}\right)^{2}}}\times 10^{-27}\times \left(3\times 10^{8}\right)^{2}$$

Kerro 334 ja \frac{1}{1000000000000000000000000000}, niin saadaan \frac{167}{500000000000000000000000000}.

$$167\sqrt{\frac{\frac{78125000000000051}{78125000000000000}}{\frac{167}{500000000000000000000000000}\times \left(3\times 10^{8}\right)^{2}}}\times 10^{-27}\times \left(3\times 10^{8}\right)^{2}$$

Laske 10 potenssiin 8, jolloin ratkaisuksi tulee 100000000.

$$167\sqrt{\frac{\frac{78125000000000051}{78125000000000000}}{\frac{167}{500000000000000000000000000}\times \left(3\times 100000000\right)^{2}}}\times 10^{-27}\times \left(3\times 10^{8}\right)^{2}$$

Kerro 3 ja 100000000, niin saadaan 300000000.

$$167\sqrt{\frac{\frac{78125000000000051}{78125000000000000}}{\frac{167}{500000000000000000000000000}\times 300000000^{2}}}\times 10^{-27}\times \left(3\times 10^{8}\right)^{2}$$

Laske 300000000 potenssiin 2, jolloin ratkaisuksi tulee 90000000000000000.

$$167\sqrt{\frac{\frac{78125000000000051}{78125000000000000}}{\frac{167}{500000000000000000000000000}\times 90000000000000000}}\times 10^{-27}\times \left(3\times 10^{8}\right)^{2}$$

Kerro \frac{167}{500000000000000000000000000} ja 90000000000000000, niin saadaan \frac{1503}{50000000000}.

$$167\sqrt{\frac{\frac{78125000000000051}{78125000000000000}}{\frac{1503}{50000000000}}}\times 10^{-27}\times \left(3\times 10^{8}\right)^{2}$$

Jaa \frac{78125000000000051}{78125000000000000} luvulla \frac{1503}{50000000000} kertomalla \frac{78125000000000051}{78125000000000000} luvun \frac{1503}{50000000000} käänteisluvulla.

$$167\sqrt{\frac{78125000000000051}{78125000000000000}\times \frac{50000000000}{1503}}\times 10^{-27}\times \left(3\times 10^{8}\right)^{2}$$

Kerro \frac{78125000000000051}{78125000000000000} ja \frac{50000000000}{1503}, niin saadaan \frac{78125000000000051}{2348437500}.

$$167\sqrt{\frac{78125000000000051}{2348437500}}\times 10^{-27}\times \left(3\times 10^{8}\right)^{2}$$

Kirjoita jakolaskun \sqrt{\frac{78125000000000051}{2348437500}} neliöjuuri uudelleen neliöjuurien \frac{\sqrt{78125000000000051}}{\sqrt{2348437500}} jakolaskuna.

$$167\times \frac{\sqrt{78125000000000051}}{\sqrt{2348437500}}\times 10^{-27}\times \left(3\times 10^{8}\right)^{2}$$

Jaa 2348437500=3750^{2}\times 167 tekijöihin. Kirjoita tuotteen neliö juuri \sqrt{3750^{2}\times 167} neliö juuren tulo \sqrt{3750^{2}}\sqrt{167}. Ota luvun 3750^{2} neliöjuuri.

$$167\times \frac{\sqrt{78125000000000051}}{3750\sqrt{167}}\times 10^{-27}\times \left(3\times 10^{8}\right)^{2}$$

Muunna rationaaliluvuksi nimittäjä \frac{\sqrt{78125000000000051}}{3750\sqrt{167}} kertomalla osoittaja ja nimittäjä \sqrt{167}.

$$167\times \frac{\sqrt{78125000000000051}\sqrt{167}}{3750\left(\sqrt{167}\right)^{2}}\times 10^{-27}\times \left(3\times 10^{8}\right)^{2}$$

Luvun \sqrt{167} neliö on 167.

$$167\times \frac{\sqrt{78125000000000051}\sqrt{167}}{3750\times 167}\times 10^{-27}\times \left(3\times 10^{8}\right)^{2}$$

Jos haluat kertoa \sqrt{78125000000000051} ja \sqrt{167}, kerro numerot neliö pääkansiossa.

$$167\times \frac{\sqrt{13046875000000008517}}{3750\times 167}\times 10^{-27}\times \left(3\times 10^{8}\right)^{2}$$

Kerro 3750 ja 167, niin saadaan 626250.

$$167\times \frac{\sqrt{13046875000000008517}}{626250}\times 10^{-27}\times \left(3\times 10^{8}\right)^{2}$$

Laske 10 potenssiin -27, jolloin ratkaisuksi tulee \frac{1}{1000000000000000000000000000}.

$$167\times \frac{\sqrt{13046875000000008517}}{626250}\times \frac{1}{1000000000000000000000000000}\times \left(3\times 10^{8}\right)^{2}$$

Kerro 167 ja \frac{1}{1000000000000000000000000000}, niin saadaan \frac{167}{1000000000000000000000000000}.

$$\frac{167}{1000000000000000000000000000}\times \frac{\sqrt{13046875000000008517}}{626250}\times \left(3\times 10^{8}\right)^{2}$$

Laske 10 potenssiin 8, jolloin ratkaisuksi tulee 100000000.

$$\frac{167}{1000000000000000000000000000}\times \frac{\sqrt{13046875000000008517}}{626250}\times \left(3\times 100000000\right)^{2}$$

Kerro 3 ja 100000000, niin saadaan 300000000.

$$\frac{167}{1000000000000000000000000000}\times \frac{\sqrt{13046875000000008517}}{626250}\times 300000000^{2}$$

Laske 300000000 potenssiin 2, jolloin ratkaisuksi tulee 90000000000000000.

$$\frac{167}{1000000000000000000000000000}\times \frac{\sqrt{13046875000000008517}}{626250}\times 90000000000000000$$

Kerro \frac{167}{1000000000000000000000000000} ja 90000000000000000, niin saadaan \frac{1503}{100000000000}.

$$\frac{1503}{100000000000}\times \frac{\sqrt{13046875000000008517}}{626250}$$

Kerro \frac{1503}{100000000000} ja \frac{\sqrt{13046875000000008517}}{626250} kertomalla osoittajat keskenään ja nimittäjät keskenään.

$$\frac{1503\sqrt{13046875000000008517}}{100000000000\times 626250}$$

Supista 501 sekä osoittajasta että nimittäjästä.

$$\frac{3\sqrt{13046875000000008517}}{1250\times 100000000000}$$

Kerro 1250 ja 100000000000, niin saadaan 125000000000000.

$$\frac{3\sqrt{13046875000000008517}}{125000000000000}$$