सोडोवचें frac{4*(6-3sqrt{3})^2+1}{12-6sqrt{3}}

$$\frac { 4 \times ( 6 - 3 \sqrt { 3 } ) ^ { 2 } + 1 } { 12 - 6 \sqrt { 3 } }$$

मूल्यांकन करचें

$$-\frac{35\sqrt{3}}{6}+\frac{37}{3}\approx 2.229703623$$

सोडोवणी पांवडे

बायनोमियल प्रमेयाचो वापर करून \left(a-b\right)^{2}=a^{2}-2ab+b^{2} विस्तारावचें \left(6-3\sqrt{3}\right)^{2}.

$$\frac{4\left(36-36\sqrt{3}+9\left(\sqrt{3}\right)^{2}\right)+1}{12-6\sqrt{3}}$$

\sqrt{3} चो वर्ग 3 आसा.

$$\frac{4\left(36-36\sqrt{3}+9\times 3\right)+1}{12-6\sqrt{3}}$$

27 मेळोवंक 9 आनी 3 गुणचें.

$$\frac{4\left(36-36\sqrt{3}+27\right)+1}{12-6\sqrt{3}}$$

63 मेळोवंक 36 आनी 27 ची बेरीज करची.

$$\frac{4\left(63-36\sqrt{3}\right)+1}{12-6\sqrt{3}}$$

न्युमरेटर आनी डिनोमिनेटर 12+6\sqrt{3} न गुणून \frac{4\left(63-36\sqrt{3}\right)+1}{12-6\sqrt{3}} चो डिनोमिनेटर रेशनलायझ तर्कसंगत करचो.

$$\frac{\left(4\left(63-36\sqrt{3}\right)+1\right)\left(12+6\sqrt{3}\right)}{\left(12-6\sqrt{3}\right)\left(12+6\sqrt{3}\right)}$$

विचारांत घेयात \left(12-6\sqrt{3}\right)\left(12+6\sqrt{3}\right). नेम वापरून गुणाकार विभिन्न चवकोनांत रुपांतरण करूं येताः \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$\frac{\left(4\left(63-36\sqrt{3}\right)+1\right)\left(12+6\sqrt{3}\right)}{12^{2}-\left(-6\sqrt{3}\right)^{2}}$$

144 मेळोवंक 2 चो 12 पॉवर मेजचो.

$$\frac{\left(4\left(63-36\sqrt{3}\right)+1\right)\left(12+6\sqrt{3}\right)}{144-\left(-6\sqrt{3}\right)^{2}}$$

\left(-6\sqrt{3}\right)^{2} विस्तारीत करचो.

$$\frac{\left(4\left(63-36\sqrt{3}\right)+1\right)\left(12+6\sqrt{3}\right)}{144-\left(-6\right)^{2}\left(\sqrt{3}\right)^{2}}$$

36 मेळोवंक 2 चो -6 पॉवर मेजचो.

$$\frac{\left(4\left(63-36\sqrt{3}\right)+1\right)\left(12+6\sqrt{3}\right)}{144-36\left(\sqrt{3}\right)^{2}}$$

\sqrt{3} चो वर्ग 3 आसा.

$$\frac{\left(4\left(63-36\sqrt{3}\right)+1\right)\left(12+6\sqrt{3}\right)}{144-36\times 3}$$

108 मेळोवंक 36 आनी 3 गुणचें.

$$\frac{\left(4\left(63-36\sqrt{3}\right)+1\right)\left(12+6\sqrt{3}\right)}{144-108}$$

36 मेळोवंक 144 आनी 108 वजा करचे.

$$\frac{\left(4\left(63-36\sqrt{3}\right)+1\right)\left(12+6\sqrt{3}\right)}{36}$$

63-36\sqrt{3} न 4 गुणपाक विभाजक विशमाचो वापर करचो.

$$\frac{\left(252-144\sqrt{3}+1\right)\left(12+6\sqrt{3}\right)}{36}$$

253 मेळोवंक 252 आनी 1 ची बेरीज करची.

$$\frac{\left(253-144\sqrt{3}\right)\left(12+6\sqrt{3}\right)}{36}$$

वितरक गूणधर्माचो वापर करून 253-144\sqrt{3} क 12+6\sqrt{3} न गुणचें आनी संज्ञां भशेन एकठावणी करची.

$$\frac{3036-210\sqrt{3}-864\left(\sqrt{3}\right)^{2}}{36}$$

\sqrt{3} चो वर्ग 3 आसा.

$$\frac{3036-210\sqrt{3}-864\times 3}{36}$$

-2592 मेळोवंक -864 आनी 3 गुणचें.

$$\frac{3036-210\sqrt{3}-2592}{36}$$

444 मेळोवंक 3036 आनी 2592 वजा करचे.

$$\frac{444-210\sqrt{3}}{36}$$