ແກ້ 6*62*6*10^-24/sqrt{2*167*10^-27*81*9*10^-16}

$$\frac { 6 \cdot 62 \cdot 6 \times 10 ^ { - 24 } } { \sqrt { 2 \times 167 \times 10 ^ { - 27 } \times 81 \cdot 9 \times 10 ^ { - 16 } } }$$

ປະເມີນ

$$\frac{31\sqrt{835}}{62625}\approx 0,01430399$$

ຂັ້ນຕອນການແກ້

ເພື່ອຄູນເລກກຳລັງຂອງຖານດຽວກັນ, ໃຫ້ບວກເລກກຳລັງຂອງພວກມັນ. ບວກ -27 ແລະ -16 ເພື່ອໃຫ້ໄດ້ -43.

$$\frac{6\times 62\times 6\times 10^{-24}}{\sqrt{2\times 167\times 10^{-43}\times 81\times 9}}$$

ຄູນ 6 ກັບ 62 ເພື່ອໃຫ້ໄດ້ 372.

$$\frac{372\times 6\times 10^{-24}}{\sqrt{2\times 167\times 10^{-43}\times 81\times 9}}$$

ຄູນ 372 ກັບ 6 ເພື່ອໃຫ້ໄດ້ 2232.

$$\frac{2232\times 10^{-24}}{\sqrt{2\times 167\times 10^{-43}\times 81\times 9}}$$

ຄຳນວນ 10 ກຳລັງ -24 ແລະ ໄດ້ \frac{1}{1000000000000000000000000}.

$$\frac{2232\times \frac{1}{1000000000000000000000000}}{\sqrt{2\times 167\times 10^{-43}\times 81\times 9}}$$

ຄູນ 2232 ກັບ \frac{1}{1000000000000000000000000} ເພື່ອໃຫ້ໄດ້ \frac{279}{125000000000000000000000}.

$$\frac{\frac{279}{125000000000000000000000}}{\sqrt{2\times 167\times 10^{-43}\times 81\times 9}}$$

ຄູນ 2 ກັບ 167 ເພື່ອໃຫ້ໄດ້ 334.

$$\frac{\frac{279}{125000000000000000000000}}{\sqrt{334\times 10^{-43}\times 81\times 9}}$$

ຄຳນວນ 10 ກຳລັງ -43 ແລະ ໄດ້ \frac{1}{10000000000000000000000000000000000000000000}.

$$\frac{\frac{279}{125000000000000000000000}}{\sqrt{334\times \frac{1}{10000000000000000000000000000000000000000000}\times 81\times 9}}$$

ຄູນ 334 ກັບ \frac{1}{10000000000000000000000000000000000000000000} ເພື່ອໃຫ້ໄດ້ \frac{167}{5000000000000000000000000000000000000000000}.

$$\frac{\frac{279}{125000000000000000000000}}{\sqrt{\frac{167}{5000000000000000000000000000000000000000000}\times 81\times 9}}$$

ຄູນ \frac{167}{5000000000000000000000000000000000000000000} ກັບ 81 ເພື່ອໃຫ້ໄດ້ \frac{13527}{5000000000000000000000000000000000000000000}.

$$\frac{\frac{279}{125000000000000000000000}}{\sqrt{\frac{13527}{5000000000000000000000000000000000000000000}\times 9}}$$

ຄູນ \frac{13527}{5000000000000000000000000000000000000000000} ກັບ 9 ເພື່ອໃຫ້ໄດ້ \frac{121743}{5000000000000000000000000000000000000000000}.

$$\frac{\frac{279}{125000000000000000000000}}{\sqrt{\frac{121743}{5000000000000000000000000000000000000000000}}}$$

ຂຽນຮາກຂັ້ນສອງຂອງການແບ່ງ \sqrt{\frac{121743}{5000000000000000000000000000000000000000000}} ຄືນໃໝ່ເປັນຕົວແບ່ງຂອງຮາກຂັ້ນສອງ \frac{\sqrt{121743}}{\sqrt{5000000000000000000000000000000000000000000}}.

$$\frac{\frac{279}{125000000000000000000000}}{\frac{\sqrt{121743}}{\sqrt{5000000000000000000000000000000000000000000}}}$$

ຕົວປະກອບ 121743=27^{2}\times 167. ຂຽນຮາກຂັ້ນສອງຂອງຜົນຄູນ \sqrt{27^{2}\times 167} ເປັນຜົນຄູນຂອງຮາກຂັ້ນສອງ \sqrt{27^{2}}\sqrt{167}. ເອົາຮາກຂັ້ນສອງຂອງ 27^{2}.

$$\frac{\frac{279}{125000000000000000000000}}{\frac{27\sqrt{167}}{\sqrt{5000000000000000000000000000000000000000000}}}$$

ຕົວປະກອບ 5000000000000000000000000000000000000000000=1000000000000000000000^{2}\times 5. ຂຽນຮາກຂັ້ນສອງຂອງຜົນຄູນ \sqrt{1000000000000000000000^{2}\times 5} ເປັນຜົນຄູນຂອງຮາກຂັ້ນສອງ \sqrt{1000000000000000000000^{2}}\sqrt{5}. ເອົາຮາກຂັ້ນສອງຂອງ 1000000000000000000000^{2}.

$$\frac{\frac{279}{125000000000000000000000}}{\frac{27\sqrt{167}}{1000000000000000000000\sqrt{5}}}$$

ໃຊ້ເຫດຜົນຕັດສິນຕົວຫານຂອງ \frac{27\sqrt{167}}{1000000000000000000000\sqrt{5}} ໂດຍການຫານຕົວເສດ ແລະ ຕົວຫານໂດຍ \sqrt{5}.

$$\frac{\frac{279}{125000000000000000000000}}{\frac{27\sqrt{167}\sqrt{5}}{1000000000000000000000\left(\sqrt{5}\right)^{2}}}$$

ຮາກຂອງ \sqrt{5} ແມ່ນ 5.

$$\frac{\frac{279}{125000000000000000000000}}{\frac{27\sqrt{167}\sqrt{5}}{1000000000000000000000\times 5}}$$

ເພື່ອຄູນ \sqrt{167} ແລະ \sqrt{5}, ໃຫ້ຄູນຈຳນວນພາຍໃຕ້ຮາກຂັ້ນສູງ.

$$\frac{\frac{279}{125000000000000000000000}}{\frac{27\sqrt{835}}{1000000000000000000000\times 5}}$$

ຄູນ 1000000000000000000000 ກັບ 5 ເພື່ອໃຫ້ໄດ້ 5000000000000000000000.

$$\frac{\frac{279}{125000000000000000000000}}{\frac{27\sqrt{835}}{5000000000000000000000}}$$

ຫານ \frac{279}{125000000000000000000000} ດ້ວຍ \frac{27\sqrt{835}}{5000000000000000000000} ໂດຍການຄູນ \frac{279}{125000000000000000000000} ໂດຍຕົວເລກທີ່ກັບກັນຂອງ \frac{27\sqrt{835}}{5000000000000000000000}.

$$\frac{279\times 5000000000000000000000}{125000000000000000000000\times 27\sqrt{835}}$$

ຍົກເລີກ 9\times 5000000000000000000000 ທັງໃນຕົວເສດ ແລະ ຕົວຫານ.

$$\frac{31}{3\times 25\sqrt{835}}$$

ໃຊ້ເຫດຜົນຕັດສິນຕົວຫານຂອງ \frac{31}{3\times 25\sqrt{835}} ໂດຍການຫານຕົວເສດ ແລະ ຕົວຫານໂດຍ \sqrt{835}.

$$\frac{31\sqrt{835}}{3\times 25\left(\sqrt{835}\right)^{2}}$$

ຮາກຂອງ \sqrt{835} ແມ່ນ 835.

$$\frac{31\sqrt{835}}{3\times 25\times 835}$$

ຄູນ 3 ກັບ 25 ເພື່ອໃຫ້ໄດ້ 75.

$$\frac{31\sqrt{835}}{75\times 835}$$

ຄູນ 75 ກັບ 835 ເພື່ອໃຫ້ໄດ້ 62625.

$$\frac{31\sqrt{835}}{62625}$$