Lutasin ang 13/2sqrt{96}+sqrt[2]{486}-2sqrt[3]{6}+9sqrt[4]{243}

$$1 \frac { 3 } { 2 } \sqrt { 96 } + \sqrt[ 2 ] { 486 } - 2 \sqrt[ 3 ] { 6 } + 9 \sqrt[ 4 ] { 243 }$$

I-evaluate

$$19\sqrt{6}+27\sqrt[4]{3}-2\sqrt[3]{6}\approx 78.440062277$$

Mga Hakbang ng Solution

I-multiply ang 1 at 2 para makuha ang 2.

$$\frac{2+3}{2}\sqrt{96}+\sqrt[2]{486}-2\sqrt[3]{6}+9\sqrt[4]{243}$$

Idagdag ang 2 at 3 para makuha ang 5.

$$\frac{5}{2}\sqrt{96}+\sqrt[2]{486}-2\sqrt[3]{6}+9\sqrt[4]{243}$$

I-factor out ang 96=4^{2}\times 6. I-rewrite ang square root ng product na \sqrt{4^{2}\times 6} bilang product ng mga square root na \sqrt{4^{2}}\sqrt{6}. Kunin ang square root ng 4^{2}.

$$\frac{5}{2}\times 4\sqrt{6}+\sqrt[2]{486}-2\sqrt[3]{6}+9\sqrt[4]{243}$$

I-multiply ang \frac{5}{2} at 4 para makuha ang 10.

$$10\sqrt{6}+\sqrt[2]{486}-2\sqrt[3]{6}+9\sqrt[4]{243}$$

I-factor

$$19 \sqrt{6} + 27 \sqrt[4]{3} - 2 \sqrt[3]{6} = 78.440062277$$