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

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

Vlerëso

$$\frac{3\sqrt{13046875000000008517}}{125000000000000}\approx 0.000086689$$

Hapat e zgjidhjes

Thjeshto 2 dhe 2.

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

Shumëzo 408 me 16 për të marrë 6528.

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

Llogarit 10 në fuqi të -19 dhe merr \frac{1}{10000000000000000000}.

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

Shumëzo 6528 me \frac{1}{10000000000000000000} për të marrë \frac{51}{78125000000000000}.

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

Shto 1 dhe \frac{51}{78125000000000000} për të marrë \frac{78125000000000051}{78125000000000000}.

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

Shumëzo 2 me 167 për të marrë 334.

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

Llogarit 10 në fuqi të -27 dhe merr \frac{1}{1000000000000000000000000000}.

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

Shumëzo 334 me \frac{1}{1000000000000000000000000000} për të marrë \frac{167}{500000000000000000000000000}.

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

Llogarit 10 në fuqi të 8 dhe merr 100000000.

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

Shumëzo 3 me 100000000 për të marrë 300000000.

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

Llogarit 300000000 në fuqi të 2 dhe merr 90000000000000000.

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

Shumëzo \frac{167}{500000000000000000000000000} me 90000000000000000 për të marrë \frac{1503}{50000000000}.

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

Pjesëto \frac{78125000000000051}{78125000000000000} me \frac{1503}{50000000000} duke shumëzuar \frac{78125000000000051}{78125000000000000} me të anasjelltën e \frac{1503}{50000000000}.

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

Shumëzo \frac{78125000000000051}{78125000000000000} me \frac{50000000000}{1503} për të marrë \frac{78125000000000051}{2348437500}.

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

Rishkruaj rrënjën katrore të pjesëtimit \sqrt{\frac{78125000000000051}{2348437500}} si pjesëtim të rrënjëve katrore \frac{\sqrt{78125000000000051}}{\sqrt{2348437500}}.

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

Faktorizo 2348437500=3750^{2}\times 167. Rishkruaj rrënjën katrore të produktit \sqrt{3750^{2}\times 167} si produkt i rrënjëve katrore \sqrt{3750^{2}}\sqrt{167}. Gjej rrënjën katrore të 3750^{2}.

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

Racionalizo emëruesin e \frac{\sqrt{78125000000000051}}{3750\sqrt{167}} duke shumëzuar numëruesin dhe emëruesin me \sqrt{167}.

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

Katrori i \sqrt{167} është 167.

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

Për të shumëzuar \sqrt{78125000000000051} dhe \sqrt{167}, shumëzo numrat nën rrënjën katrore.

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

Shumëzo 3750 me 167 për të marrë 626250.

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

Llogarit 10 në fuqi të -27 dhe merr \frac{1}{1000000000000000000000000000}.

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

Shumëzo 167 me \frac{1}{1000000000000000000000000000} për të marrë \frac{167}{1000000000000000000000000000}.

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

Llogarit 10 në fuqi të 8 dhe merr 100000000.

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

Shumëzo 3 me 100000000 për të marrë 300000000.

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

Llogarit 300000000 në fuqi të 2 dhe merr 90000000000000000.

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

Shumëzo \frac{167}{1000000000000000000000000000} me 90000000000000000 për të marrë \frac{1503}{100000000000}.

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

Shumëzo \frac{1503}{100000000000} herë \frac{\sqrt{13046875000000008517}}{626250} duke shumëzuar numëruesin me numëruesin dhe emëruesin me emëruesin.

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

Thjeshto 501 në numërues dhe emërues.

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

Shumëzo 1250 me 100000000000 për të marrë 125000000000000.

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