सोडोवचें [(sqrt{2})^{2}*(2/sqrt{3})^2][(1/2)^2+4*1^2-2^2]

$$[ ( \sqrt { 2 } ) ^ { 2 } \times ( \frac { 2 } { \sqrt { 3 } } ) ^ { 2 } ] [ ( \frac { 1 } { 2 } ) ^ { 2 } + 4 \times 1 ^ { 2 } - 2 ^ { 2 } ]$$

मूल्यांकन करचें

$$\frac{2}{3}\approx 0.666666667$$

सोडोवणी पांवडे

\sqrt{2} चो वर्ग 2 आसा.

$$2\times \left(\frac{2}{\sqrt{3}}\right)^{2}\left(\left(\frac{1}{2}\right)^{2}+4\times 1^{2}-2^{2}\right)$$

न्युमरेटर आनी डिनोमिनेटर \sqrt{3} न गुणून \frac{2}{\sqrt{3}} चो डिनोमिनेटर रेशनलायझ तर्कसंगत करचो.

$$2\times \left(\frac{2\sqrt{3}}{\left(\sqrt{3}\right)^{2}}\right)^{2}\left(\left(\frac{1}{2}\right)^{2}+4\times 1^{2}-2^{2}\right)$$

\sqrt{3} चो वर्ग 3 आसा.

$$2\times \left(\frac{2\sqrt{3}}{3}\right)^{2}\left(\left(\frac{1}{2}\right)^{2}+4\times 1^{2}-2^{2}\right)$$

\frac{2\sqrt{3}}{3} पॉवर दिवंक, न्युमरेटर आनी डिनोमिनेटर दोनूय पॉवर मेरेन वाडोवचे आनी मागीर भाग लावचो.

$$2\times \frac{\left(2\sqrt{3}\right)^{2}}{3^{2}}\left(\left(\frac{1}{2}\right)^{2}+4\times 1^{2}-2^{2}\right)$$

\frac{1}{4} मेळोवंक 2 चो \frac{1}{2} पॉवर मेजचो.

$$2\times \frac{\left(2\sqrt{3}\right)^{2}}{3^{2}}\left(\frac{1}{4}+4\times 1^{2}-2^{2}\right)$$

1 मेळोवंक 2 चो 1 पॉवर मेजचो.

$$2\times \frac{\left(2\sqrt{3}\right)^{2}}{3^{2}}\left(\frac{1}{4}+4\times 1-2^{2}\right)$$

4 मेळोवंक 4 आनी 1 गुणचें.

$$2\times \frac{\left(2\sqrt{3}\right)^{2}}{3^{2}}\left(\frac{1}{4}+4-2^{2}\right)$$

\frac{17}{4} मेळोवंक \frac{1}{4} आनी 4 ची बेरीज करची.

$$2\times \frac{\left(2\sqrt{3}\right)^{2}}{3^{2}}\left(\frac{17}{4}-2^{2}\right)$$

4 मेळोवंक 2 चो 2 पॉवर मेजचो.

$$2\times \frac{\left(2\sqrt{3}\right)^{2}}{3^{2}}\left(\frac{17}{4}-4\right)$$

\frac{1}{4} मेळोवंक \frac{17}{4} आनी 4 वजा करचे.

$$2\times \frac{\left(2\sqrt{3}\right)^{2}}{3^{2}}\times \frac{1}{4}$$

\frac{1}{2} मेळोवंक 2 आनी \frac{1}{4} गुणचें.

$$\frac{1}{2}\times \frac{\left(2\sqrt{3}\right)^{2}}{3^{2}}$$

\left(2\sqrt{3}\right)^{2} विस्तारीत करचो.

$$\frac{1}{2}\times \frac{2^{2}\left(\sqrt{3}\right)^{2}}{3^{2}}$$

4 मेळोवंक 2 चो 2 पॉवर मेजचो.

$$\frac{1}{2}\times \frac{4\left(\sqrt{3}\right)^{2}}{3^{2}}$$

\sqrt{3} चो वर्ग 3 आसा.

$$\frac{1}{2}\times \frac{4\times 3}{3^{2}}$$

12 मेळोवंक 4 आनी 3 गुणचें.

$$\frac{1}{2}\times \frac{12}{3^{2}}$$

9 मेळोवंक 2 चो 3 पॉवर मेजचो.

$$\frac{1}{2}\times \frac{12}{9}$$

3 भायर काडून आनी रद्द करून एकदम उण्या संज्ञेत अपुर्णांक \frac{12}{9} उणो करचो.

$$\frac{1}{2}\times \frac{4}{3}$$

\frac{2}{3} मेळोवंक \frac{1}{2} आनी \frac{4}{3} गुणचें.

$$\frac{2}{3}$$

गुणकपद

$$\frac{2}{3} = 0.6666666666666666$$