frac{sqrt{24}+sqrt{8}}{sqrt{2}}-1 eching

$$\frac{ \sqrt{ 24 } + \sqrt{ 8 } }{ \sqrt{ 2 } } -1$$

Baholash

$$2\sqrt{3}+1\approx 4,464101615$$

Qisqa yechim qadamlari

Faktor: 24=2^{2}\times 6. \sqrt{2^{2}\times 6} koʻpaytmasining kvadrat ildizini \sqrt{2^{2}}\sqrt{6} kvadrat ildizlarining koʻpaytmasi sifatida qayta yozing. 2^{2} ning kvadrat ildizini chiqarish.

$$\frac{2\sqrt{6}+\sqrt{8}}{\sqrt{2}}-1$$

Faktor: 8=2^{2}\times 2. \sqrt{2^{2}\times 2} koʻpaytmasining kvadrat ildizini \sqrt{2^{2}}\sqrt{2} kvadrat ildizlarining koʻpaytmasi sifatida qayta yozing. 2^{2} ning kvadrat ildizini chiqarish.

$$\frac{2\sqrt{6}+2\sqrt{2}}{\sqrt{2}}-1$$

\frac{2\sqrt{6}+2\sqrt{2}}{\sqrt{2}} maxrajini \sqrt{2} orqali surat va maxrajini koʻpaytirish orqali ratsionallashtiring.

$$\frac{\left(2\sqrt{6}+2\sqrt{2}\right)\sqrt{2}}{\left(\sqrt{2}\right)^{2}}-1$$

\sqrt{2} kvadrati – 2.

$$\frac{\left(2\sqrt{6}+2\sqrt{2}\right)\sqrt{2}}{2}-1$$

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. 1 ni \frac{2}{2} marotabaga ko'paytirish.

$$\frac{\left(2\sqrt{6}+2\sqrt{2}\right)\sqrt{2}}{2}-\frac{2}{2}$$

\frac{\left(2\sqrt{6}+2\sqrt{2}\right)\sqrt{2}}{2} va \frac{2}{2} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$\frac{\left(2\sqrt{6}+2\sqrt{2}\right)\sqrt{2}-2}{2}$$

\left(2\sqrt{6}+2\sqrt{2}\right)\sqrt{2}-2 ichidagi ko‘paytirishlarni bajaring.

$$\frac{4\sqrt{3}+4-2}{2}$$

4\sqrt{3}+4-2 hisob-kitobini qiling.

$$\frac{4\sqrt{3}+2}{2}$$

2\sqrt{3}+1 natijani olish uchun 4\sqrt{3}+2 ning har bir ifodasini 2 ga bo‘ling.

$$2\sqrt{3}+1$$