Datrys sqrt{5456}*sqrt{2120}divsqrt{460}=?

$$\sqrt { 5456 } \times \sqrt { 2120 } \div \sqrt { 460 } = ?$$

Enrhifo

$$\frac{4\sqrt{831358}}{23}\approx 158.571887415$$

Camau Ateb

Ffactora 5456=4^{2}\times 341. Ailysgrifennu ail isradd y lluoswm \sqrt{4^{2}\times 341} fel lluoswm ail israddau \sqrt{4^{2}}\sqrt{341}. Cymryd isradd 4^{2}.

$$\frac{4\sqrt{341}\sqrt{2120}}{\sqrt{460}}$$

Ffactora 2120=2^{2}\times 530. Ailysgrifennu ail isradd y lluoswm \sqrt{2^{2}\times 530} fel lluoswm ail israddau \sqrt{2^{2}}\sqrt{530}. Cymryd isradd 2^{2}.

$$\frac{4\sqrt{341}\times 2\sqrt{530}}{\sqrt{460}}$$

Lluosi 4 a 2 i gael 8.

$$\frac{8\sqrt{341}\sqrt{530}}{\sqrt{460}}$$

I luosi \sqrt{341} a \sqrt{530}, dylid lluosi'r rhifau dan yr ail isradd.

$$\frac{8\sqrt{180730}}{\sqrt{460}}$$

Ffactora 460=2^{2}\times 115. Ailysgrifennu ail isradd y lluoswm \sqrt{2^{2}\times 115} fel lluoswm ail israddau \sqrt{2^{2}}\sqrt{115}. Cymryd isradd 2^{2}.

$$\frac{8\sqrt{180730}}{2\sqrt{115}}$$

Canslo 2 yn y rhifiadur a'r enwadur.

$$\frac{4\sqrt{180730}}{\sqrt{115}}$$

Mae'n rhesymoli enwadur \frac{4\sqrt{180730}}{\sqrt{115}} drwy luosi'r rhifiadur a'r enwadur â \sqrt{115}.

$$\frac{4\sqrt{180730}\sqrt{115}}{\left(\sqrt{115}\right)^{2}}$$

Sgwâr \sqrt{115} yw 115.

$$\frac{4\sqrt{180730}\sqrt{115}}{115}$$

I luosi \sqrt{180730} a \sqrt{115}, dylid lluosi'r rhifau dan yr ail isradd.

$$\frac{4\sqrt{20783950}}{115}$$

Ffactora 20783950=5^{2}\times 831358. Ailysgrifennu ail isradd y lluoswm \sqrt{5^{2}\times 831358} fel lluoswm ail israddau \sqrt{5^{2}}\sqrt{831358}. Cymryd isradd 5^{2}.

$$\frac{4\times 5\sqrt{831358}}{115}$$

Lluosi 4 a 5 i gael 20.

$$\frac{20\sqrt{831358}}{115}$$

Rhannu 20\sqrt{831358} â 115 i gael \frac{4}{23}\sqrt{831358}.

$$\frac{4}{23}\sqrt{831358}$$