Whakaoti i te 4/7sqrt{147}+3/8sqrt{192}-1/5sqrt{75}

$$\frac { 4 } { 7 } \sqrt { 147 } + \frac { 3 } { 8 } \sqrt { 192 } - \frac { 1 } { 5 } \sqrt { 75 }$$

Aromātai

$$6\sqrt{3}\approx 10.392304845$$

Ngā Upane Otinga

Tauwehea te 147=7^{2}\times 3. Tuhia anō te pūtake rua o te hua \sqrt{7^{2}\times 3} hei hua o ngā pūtake rua \sqrt{7^{2}}\sqrt{3}. Tuhia te pūtakerua o te 7^{2}.

$$\frac{4}{7}\times 7\sqrt{3}+\frac{3}{8}\sqrt{192}-\frac{1}{5}\sqrt{75}$$

Me whakakore te 7 me te 7.

$$4\sqrt{3}+\frac{3}{8}\sqrt{192}-\frac{1}{5}\sqrt{75}$$

Tauwehea te 192=8^{2}\times 3. Tuhia anō te pūtake rua o te hua \sqrt{8^{2}\times 3} hei hua o ngā pūtake rua \sqrt{8^{2}}\sqrt{3}. Tuhia te pūtakerua o te 8^{2}.

$$4\sqrt{3}+\frac{3}{8}\times 8\sqrt{3}-\frac{1}{5}\sqrt{75}$$

Me whakakore te 8 me te 8.

$$4\sqrt{3}+3\sqrt{3}-\frac{1}{5}\sqrt{75}$$

Pahekotia te 4\sqrt{3} me 3\sqrt{3}, ka 7\sqrt{3}.

$$7\sqrt{3}-\frac{1}{5}\sqrt{75}$$

Tauwehea te 75=5^{2}\times 3. Tuhia anō te pūtake rua o te hua \sqrt{5^{2}\times 3} hei hua o ngā pūtake rua \sqrt{5^{2}}\sqrt{3}. Tuhia te pūtakerua o te 5^{2}.

$$7\sqrt{3}-\frac{1}{5}\times 5\sqrt{3}$$

Me whakakore te 5 me te 5.

$$7\sqrt{3}-\sqrt{3}$$

Pahekotia te 7\sqrt{3} me -\sqrt{3}, ka 6\sqrt{3}.

$$6\sqrt{3}$$