Zgjidh (54002341048623*(4+8))/(sqrt{88247711001123870*4287)+84/81}

$$\frac { ( 54002341048623 \cdot ( 4 + 8 ) ) } { ( \sqrt { 88247711001123870 \cdot 4287 } ) + \frac { 84 } { 81 } }$$

Vlerëso

$$\frac{708618719240031006\sqrt{42035326340202003410}}{137896888059032672186113}-\frac{34993516999507704}{19699555437004667455159}\approx 33316.959958538$$

Hapat e zgjidhjes

Shto 4 dhe 8 për të marrë 12.

$$\frac{54002341048623\times 12}{\sqrt{88247711001123870\times 4287}+\frac{84}{81}}$$

Shumëzo 54002341048623 me 12 për të marrë 648028092583476.

$$\frac{648028092583476}{\sqrt{88247711001123870\times 4287}+\frac{84}{81}}$$

Shumëzo 88247711001123870 me 4287 për të marrë 378317937061818030690.

$$\frac{648028092583476}{\sqrt{378317937061818030690}+\frac{84}{81}}$$

Faktorizo 378317937061818030690=3^{2}\times 42035326340202003410. Rishkruaj rrënjën katrore të produktit \sqrt{3^{2}\times 42035326340202003410} si produkt i rrënjëve katrore \sqrt{3^{2}}\sqrt{42035326340202003410}. Gjej rrënjën katrore të 3^{2}.

$$\frac{648028092583476}{3\sqrt{42035326340202003410}+\frac{84}{81}}$$

Thjeshto thyesën \frac{84}{81} në kufizat më të vogla duke zbritur dhe thjeshtuar 3.

$$\frac{648028092583476}{3\sqrt{42035326340202003410}+\frac{28}{27}}$$

Racionalizo emëruesin e \frac{648028092583476}{3\sqrt{42035326340202003410}+\frac{28}{27}} duke shumëzuar numëruesin dhe emëruesin me 3\sqrt{42035326340202003410}-\frac{28}{27}.

$$\frac{648028092583476\left(3\sqrt{42035326340202003410}-\frac{28}{27}\right)}{\left(3\sqrt{42035326340202003410}+\frac{28}{27}\right)\left(3\sqrt{42035326340202003410}-\frac{28}{27}\right)}$$

Merr parasysh \left(3\sqrt{42035326340202003410}+\frac{28}{27}\right)\left(3\sqrt{42035326340202003410}-\frac{28}{27}\right). Shumëzimi mund të shndërrohet në diferencë të katrorëve duke përdorur rregullën: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$\frac{648028092583476\left(3\sqrt{42035326340202003410}-\frac{28}{27}\right)}{\left(3\sqrt{42035326340202003410}\right)^{2}-\left(\frac{28}{27}\right)^{2}}$$

Zhvillo \left(3\sqrt{42035326340202003410}\right)^{2}.

$$\frac{648028092583476\left(3\sqrt{42035326340202003410}-\frac{28}{27}\right)}{3^{2}\left(\sqrt{42035326340202003410}\right)^{2}-\left(\frac{28}{27}\right)^{2}}$$

Llogarit 3 në fuqi të 2 dhe merr 9.

$$\frac{648028092583476\left(3\sqrt{42035326340202003410}-\frac{28}{27}\right)}{9\left(\sqrt{42035326340202003410}\right)^{2}-\left(\frac{28}{27}\right)^{2}}$$

Katrori i \sqrt{42035326340202003410} është 42035326340202003410.

$$\frac{648028092583476\left(3\sqrt{42035326340202003410}-\frac{28}{27}\right)}{9\times 42035326340202003410-\left(\frac{28}{27}\right)^{2}}$$

Shumëzo 9 me 42035326340202003410 për të marrë 378317937061818030690.

$$\frac{648028092583476\left(3\sqrt{42035326340202003410}-\frac{28}{27}\right)}{378317937061818030690-\left(\frac{28}{27}\right)^{2}}$$

Llogarit \frac{28}{27} në fuqi të 2 dhe merr \frac{784}{729}.

$$\frac{648028092583476\left(3\sqrt{42035326340202003410}-\frac{28}{27}\right)}{378317937061818030690-\frac{784}{729}}$$

Konverto 378317937061818030690 në thyesën \frac{275793776118065344373010}{729}.

$$\frac{648028092583476\left(3\sqrt{42035326340202003410}-\frac{28}{27}\right)}{\frac{275793776118065344373010}{729}-\frac{784}{729}}$$

Meqenëse \frac{275793776118065344373010}{729} dhe \frac{784}{729} kanë të njëjtin emërues, zbriti duke zbritur numëruesit e tyre.

$$\frac{648028092583476\left(3\sqrt{42035326340202003410}-\frac{28}{27}\right)}{\frac{275793776118065344373010-784}{729}}$$

Zbrit 784 nga 275793776118065344373010 për të marrë 275793776118065344372226.

$$\frac{648028092583476\left(3\sqrt{42035326340202003410}-\frac{28}{27}\right)}{\frac{275793776118065344372226}{729}}$$

Pjesëto 648028092583476\left(3\sqrt{42035326340202003410}-\frac{28}{27}\right) me \frac{275793776118065344372226}{729} për të marrë \frac{236206239746677002}{137896888059032672186113}\left(3\sqrt{42035326340202003410}-\frac{28}{27}\right).

$$\frac{236206239746677002}{137896888059032672186113}\left(3\sqrt{42035326340202003410}-\frac{28}{27}\right)$$

Përdor vetinë e shpërndarjes për të shumëzuar \frac{236206239746677002}{137896888059032672186113} me 3\sqrt{42035326340202003410}-\frac{28}{27}.

$$\frac{236206239746677002}{137896888059032672186113}\times 3\sqrt{42035326340202003410}+\frac{236206239746677002}{137896888059032672186113}\left(-\frac{28}{27}\right)$$

Shpreh \frac{236206239746677002}{137896888059032672186113}\times 3 si një thyesë të vetme.

$$\frac{236206239746677002\times 3}{137896888059032672186113}\sqrt{42035326340202003410}+\frac{236206239746677002}{137896888059032672186113}\left(-\frac{28}{27}\right)$$

Shumëzo 236206239746677002 me 3 për të marrë 708618719240031006.

$$\frac{708618719240031006}{137896888059032672186113}\sqrt{42035326340202003410}+\frac{236206239746677002}{137896888059032672186113}\left(-\frac{28}{27}\right)$$

Shumëzo \frac{236206239746677002}{137896888059032672186113} herë -\frac{28}{27} duke shumëzuar numëruesin me numëruesin dhe emëruesin me emëruesin.

$$\frac{708618719240031006}{137896888059032672186113}\sqrt{42035326340202003410}+\frac{236206239746677002\left(-28\right)}{137896888059032672186113\times 27}$$

Bëj shumëzimet në thyesën \frac{236206239746677002\left(-28\right)}{137896888059032672186113\times 27}.

$$\frac{708618719240031006}{137896888059032672186113}\sqrt{42035326340202003410}+\frac{-6613774712906956056}{3723215977593882149025051}$$

Thjeshto thyesën \frac{-6613774712906956056}{3723215977593882149025051} në kufizat më të vogla duke zbritur dhe thjeshtuar 189.

$$\frac{708618719240031006}{137896888059032672186113}\sqrt{42035326340202003410}-\frac{34993516999507704}{19699555437004667455159}$$

Faktorizo

$$\frac{8748379249876926 {(81 \sqrt{42035326340202003410} - 28)}}{137896888059032672186113} = 33316\frac{1.3237529501491374 \times 10^{23}}{1.3789688805903266 \times 10^{23}} = 33316.9599585377$$